LMFDB - Embedded newform 147.6.e.p.79.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,6,Mod(67,147)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("147.67");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	147.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$23.5764215125$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 63 x^{10} - 126 x^{9} + 2784 x^{8} - 5290 x^{7} + 62015 x^{6} - 99530 x^{5} + \cdots + 5466244 $ x^12 - 2x^11 + 63x^10 - 126x^9 + 2784x^8 - 5290x^7 + 62015x^6 - 99530x^5 + 973971x^4 - 1176024x^3 + 5644794x^2 + 4339328*x + 5466244
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8}\cdot 7^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.6
Root			$-2.80572 - 4.85966i$ of defining polynomial
Character	$\chi$	$=$	147.79
Dual form			147.6.e.p.67.6

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.59404 - 9.68915i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-46.5865 - 80.6901i) q^{4} +(31.1575 - 53.9664i) q^{5} -100.693 q^{6} -684.407 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})$	\(q+(5.59404 - 9.68915i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-46.5865 - 80.6901i) q^{4} +(31.1575 - 53.9664i) q^{5} -100.693 q^{6} -684.407 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-348.592 - 603.780i) q^{10} +(86.7474 + 150.251i) q^{11} +(-419.278 + 726.211i) q^{12} +348.244 q^{13} -560.835 q^{15} +(-2337.83 + 4049.24i) q^{16} +(-499.603 - 865.338i) q^{17} +(453.117 + 784.821i) q^{18} +(1021.09 - 1768.57i) q^{19} -5806.07 q^{20} +1941.07 q^{22} +(974.835 - 1688.46i) q^{23} +(3079.83 + 5334.43i) q^{24} +(-379.079 - 656.585i) q^{25} +(1948.09 - 3374.19i) q^{26} +729.000 q^{27} +738.129 q^{29} +(-3137.33 + 5434.02i) q^{30} +(1229.99 + 2130.41i) q^{31} +(15205.3 + 26336.4i) q^{32} +(780.727 - 1352.26i) q^{33} -11179.2 q^{34} +7547.01 q^{36} +(-4393.26 + 7609.35i) q^{37} +(-11424.0 - 19786.9i) q^{38} +(-1567.10 - 2714.30i) q^{39} +(-21324.4 + 36935.0i) q^{40} +17617.4 q^{41} -10317.1 q^{43} +(8082.51 - 13999.3i) q^{44} +(2523.76 + 4371.28i) q^{45} +(-10906.5 - 18890.7i) q^{46} +(37.5291 - 65.0023i) q^{47} +42081.0 q^{48} -8482.34 q^{50} +(-4496.43 + 7788.04i) q^{51} +(-16223.5 - 28099.9i) q^{52} +(-13852.8 - 23993.7i) q^{53} +(4078.05 - 7063.39i) q^{54} +10811.3 q^{55} -18379.5 q^{57} +(4129.12 - 7151.85i) q^{58} +(1728.79 + 2994.35i) q^{59} +(26127.3 + 45253.9i) q^{60} +(-7978.20 + 13818.6i) q^{61} +27522.5 q^{62} +190615. q^{64} +(10850.4 - 18793.5i) q^{65} +(-8734.83 - 15129.2i) q^{66} +(-7206.58 - 12482.2i) q^{67} +(-46549.5 + 80626.1i) q^{68} -17547.0 q^{69} -30337.6 q^{71} +(27718.5 - 48009.8i) q^{72} +(-42940.5 - 74375.0i) q^{73} +(49152.1 + 85133.9i) q^{74} +(-3411.71 + 5909.26i) q^{75} -190275. q^{76} -35065.6 q^{78} +(-3806.63 + 6593.27i) q^{79} +(145682. + 252329. i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(98552.2 - 170697. i) q^{82} +63725.4 q^{83} -62265.5 q^{85} +(-57714.1 + 99963.8i) q^{86} +(-3321.58 - 5753.15i) q^{87} +(-59370.6 - 102833. i) q^{88} +(-23195.7 + 40176.1i) q^{89} +56472.0 q^{90} -181657. q^{92} +(11070.0 - 19173.7i) q^{93} +(-419.878 - 727.251i) q^{94} +(-63629.0 - 110209. i) q^{95} +(136848. - 237027. i) q^{96} +21461.2 q^{97} -14053.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 54 q^{3} - 150 q^{4} - 100 q^{5} + 36 q^{6} - 228 q^{8} - 486 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 - 54 * q^3 - 150 * q^4 - 100 * q^5 + 36 * q^6 - 228 * q^8 - 486 * q^9	\( 12 q - 2 q^{2} - 54 q^{3} - 150 q^{4} - 100 q^{5} + 36 q^{6} - 228 q^{8} - 486 q^{9} - 864 q^{10} - 604 q^{11} - 1350 q^{12} + 2704 q^{13} + 1800 q^{15} - 4578 q^{16} - 3028 q^{17} - 162 q^{18} - 1728 q^{19} + 904 q^{20} - 8232 q^{22} + 4484 q^{23} + 1026 q^{24} - 4806 q^{25} - 14172 q^{26} + 8748 q^{27} - 10640 q^{29} - 7776 q^{30} - 3976 q^{31} + 37326 q^{32} - 5436 q^{33} - 32672 q^{34} + 24300 q^{36} - 22680 q^{37} - 52744 q^{38} - 12168 q^{39} - 100600 q^{40} + 57512 q^{41} - 13536 q^{43} + 64940 q^{44} - 8100 q^{45} - 540 q^{46} - 51552 q^{47} + 82404 q^{48} - 81244 q^{50} - 27252 q^{51} - 119296 q^{52} - 80884 q^{53} - 1458 q^{54} + 23312 q^{55} + 31104 q^{57} + 70464 q^{58} - 8872 q^{59} - 4068 q^{60} - 50896 q^{61} + 23648 q^{62} + 399180 q^{64} - 3492 q^{65} + 37044 q^{66} - 6480 q^{67} - 37348 q^{68} - 80712 q^{69} - 221704 q^{71} + 9234 q^{72} - 64232 q^{73} + 27464 q^{74} - 43254 q^{75} - 389728 q^{76} + 255096 q^{78} - 111696 q^{79} + 308940 q^{80} - 39366 q^{81} + 189640 q^{82} + 202256 q^{83} - 46584 q^{85} - 3824 q^{86} + 47880 q^{87} + 97788 q^{88} + 35012 q^{89} + 139968 q^{90} - 898520 q^{92} - 35784 q^{93} + 121016 q^{94} + 119080 q^{95} + 335934 q^{96} + 141904 q^{97} + 97848 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 54 * q^3 - 150 * q^4 - 100 * q^5 + 36 * q^6 - 228 * q^8 - 486 * q^9 - 864 * q^10 - 604 * q^11 - 1350 * q^12 + 2704 * q^13 + 1800 * q^15 - 4578 * q^16 - 3028 * q^17 - 162 * q^18 - 1728 * q^19 + 904 * q^20 - 8232 * q^22 + 4484 * q^23 + 1026 * q^24 - 4806 * q^25 - 14172 * q^26 + 8748 * q^27 - 10640 * q^29 - 7776 * q^30 - 3976 * q^31 + 37326 * q^32 - 5436 * q^33 - 32672 * q^34 + 24300 * q^36 - 22680 * q^37 - 52744 * q^38 - 12168 * q^39 - 100600 * q^40 + 57512 * q^41 - 13536 * q^43 + 64940 * q^44 - 8100 * q^45 - 540 * q^46 - 51552 * q^47 + 82404 * q^48 - 81244 * q^50 - 27252 * q^51 - 119296 * q^52 - 80884 * q^53 - 1458 * q^54 + 23312 * q^55 + 31104 * q^57 + 70464 * q^58 - 8872 * q^59 - 4068 * q^60 - 50896 * q^61 + 23648 * q^62 + 399180 * q^64 - 3492 * q^65 + 37044 * q^66 - 6480 * q^67 - 37348 * q^68 - 80712 * q^69 - 221704 * q^71 + 9234 * q^72 - 64232 * q^73 + 27464 * q^74 - 43254 * q^75 - 389728 * q^76 + 255096 * q^78 - 111696 * q^79 + 308940 * q^80 - 39366 * q^81 + 189640 * q^82 + 202256 * q^83 - 46584 * q^85 - 3824 * q^86 + 47880 * q^87 + 97788 * q^88 + 35012 * q^89 + 139968 * q^90 - 898520 * q^92 - 35784 * q^93 + 121016 * q^94 + 119080 * q^95 + 335934 * q^96 + 141904 * q^97 + 97848 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	5.59404	−	9.68915i	0.988895	−	1.71282i	0.365743	−	0.930716i	$-0.380815\pi$
$2$	5.59404	−	9.68915i	0.988895	−	1.71282i	0.623152	−	0.782101i	$-0.285852\pi$
$3$	−4.50000	−	7.79423i	−0.288675	−	0.500000i
$3$	−4.50000	−	7.79423i	−0.288675	−	0.500000i
$4$	−46.5865	−	80.6901i	−1.45583	−	2.52157i
$5$	31.1575	−	53.9664i	0.557362	−	0.965380i	−0.440353	−	0.897825i	$-0.645147\pi$
$5$	31.1575	−	53.9664i	0.557362	−	0.965380i	0.997716	−	0.0675552i	$-0.0215199\pi$
$6$	−100.693			−1.14188
$7$		0			0
$7$		0			0
$8$	−684.407			−3.78085
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$	−348.592	−	603.780i	−1.10235	−	1.90932i
$11$	86.7474	+	150.251i	0.216160	+	0.374400i	0.953631	−	0.300979i	$-0.0973134\pi$
$11$	86.7474	+	150.251i	0.216160	+	0.374400i	−0.737471	+	0.675379i	$0.763980\pi$
$12$	−419.278	+	726.211i	−0.840522	+	1.45583i
$13$	348.244			0.571512			0.285756	−	0.958302i	$-0.407755\pi$
$13$	348.244			0.571512			0.285756	+	0.958302i	$0.407755\pi$
$14$		0			0
$15$	−560.835			−0.643587
$16$	−2337.83	+	4049.24i	−2.28304	+	3.95434i
$17$	−499.603	−	865.338i	−0.419279	−	0.726212i	0.576588	−	0.817035i	$-0.304384\pi$
$17$	−499.603	−	865.338i	−0.419279	−	0.726212i	−0.995867	+	0.0908228i	$0.971050\pi$
$18$	453.117	+	784.821i	0.329632	+	0.570939i
$19$	1021.09	−	1768.57i	0.648901	−	1.12393i	−0.334485	−	0.942401i	$-0.608562\pi$
$19$	1021.09	−	1768.57i	0.648901	−	1.12393i	0.983386	−	0.181528i	$-0.0581042\pi$
$20$	−5806.07			−3.24569
$21$		0			0
$22$	1941.07			0.855038
$23$	974.835	−	1688.46i	0.384248	−	0.665537i	−0.607417	−	0.794383i	$-0.707794\pi$
$23$	974.835	−	1688.46i	0.384248	−	0.665537i	0.991665	+	0.128846i	$0.0411274\pi$
$24$	3079.83	+	5334.43i	1.09144	+	1.89043i
$25$	−379.079	−	656.585i	−0.121305	−	0.210107i
$26$	1948.09	−	3374.19i	0.565166	−	0.978896i
$27$	729.000			0.192450
$28$		0			0
$29$	738.129			0.162981			0.0814906	−	0.996674i	$-0.474032\pi$
$29$	738.129			0.162981			0.0814906	+	0.996674i	$0.474032\pi$
$30$	−3137.33	+	5434.02i	−0.636440	+	1.10235i
$31$	1229.99	+	2130.41i	0.229879	+	0.398162i	0.957772	−	0.287529i	$-0.0928337\pi$
$31$	1229.99	+	2130.41i	0.229879	+	0.398162i	−0.727893	+	0.685691i	$0.759500\pi$
$32$	15205.3	+	26336.4i	2.62495	+	4.54654i
$33$	780.727	−	1352.26i	0.124800	−	0.216160i
$34$	−11179.2			−1.65849
$35$		0			0
$36$	7547.01			0.970552
$37$	−4393.26	+	7609.35i	−0.527573	+	0.913783i	0.471911	+	0.881646i	$0.343565\pi$
$37$	−4393.26	+	7609.35i	−0.527573	+	0.913783i	−0.999483	+	0.0321367i	$0.989769\pi$
$38$	−11424.0	−	19786.9i	−1.28339	−	2.22290i
$39$	−1567.10	−	2714.30i	−0.164981	−	0.285756i
$40$	−21324.4	+	36935.0i	−2.10730	+	3.64996i
$41$	17617.4			1.63675			0.818374	−	0.574686i	$-0.194876\pi$
$41$	17617.4			1.63675			0.818374	+	0.574686i	$0.194876\pi$
$42$		0			0
$43$	−10317.1			−0.850914			−0.425457	−	0.904979i	$-0.639887\pi$
$43$	−10317.1			−0.850914			−0.425457	+	0.904979i	$0.639887\pi$
$44$	8082.51	−	13999.3i	0.629383	−	1.09012i
$45$	2523.76	+	4371.28i	0.185787	+	0.321793i
$46$	−10906.5	−	18890.7i	−0.759962	−	1.31629i
$47$	37.5291	−	65.0023i	0.00247813	−	0.00429224i	−0.864784	−	0.502145i	$-0.832545\pi$
$47$	37.5291	−	65.0023i	0.00247813	−	0.00429224i	0.867262	+	0.497852i	$0.165878\pi$
$48$	42081.0			2.63623
$49$		0			0
$50$	−8482.34			−0.479833
$51$	−4496.43	+	7788.04i	−0.242071	+	0.419279i
$52$	−16223.5	−	28099.9i	−0.832023	−	1.44111i
$53$	−13852.8	−	23993.7i	−0.677403	−	1.17330i	−0.975760	−	0.218842i	$-0.929772\pi$
$53$	−13852.8	−	23993.7i	−0.677403	−	1.17330i	0.298358	−	0.954454i	$-0.403561\pi$
$54$	4078.05	−	7063.39i	0.190313	−	0.329632i
$55$	10811.3			0.481917
$56$		0			0
$57$	−18379.5			−0.749286
$58$	4129.12	−	7151.85i	0.161171	−	0.279157i
$59$	1728.79	+	2994.35i	0.0646564	+	0.111988i	0.896542	−	0.442960i	$-0.146072\pi$
$59$	1728.79	+	2994.35i	0.0646564	+	0.111988i	−0.831885	+	0.554948i	$0.812738\pi$
$60$	26127.3	+	45253.9i	0.936951	+	1.62285i
$61$	−7978.20	+	13818.6i	−0.274524	+	0.475490i	−0.970015	−	0.243045i	$-0.921854\pi$
$61$	−7978.20	+	13818.6i	−0.274524	+	0.475490i	0.695491	+	0.718535i	$0.255187\pi$
$62$	27522.5			0.909304
$63$		0			0
$64$	190615.			5.81711
$65$	10850.4	−	18793.5i	0.318539	−	0.551726i
$66$	−8734.83	−	15129.2i	−0.246828	−	0.427519i
$67$	−7206.58	−	12482.2i	−0.196129	−	0.339706i	0.751141	−	0.660142i	$-0.229504\pi$
$67$	−7206.58	−	12482.2i	−0.196129	−	0.339706i	−0.947270	+	0.320436i	$0.896171\pi$
$68$	−46549.5	+	80626.1i	−1.22079	+	2.11448i
$69$	−17547.0			−0.443691
$70$		0			0
$71$	−30337.6			−0.714225			−0.357112	−	0.934061i	$-0.616239\pi$
$71$	−30337.6			−0.714225			−0.357112	+	0.934061i	$0.616239\pi$
$72$	27718.5	−	48009.8i	0.630142	−	1.09144i
$73$	−42940.5	−	74375.0i	−0.943104	−	1.63350i	−0.759504	−	0.650503i	$-0.774558\pi$
$73$	−42940.5	−	74375.0i	−0.943104	−	1.63350i	−0.183600	−	0.983001i	$-0.558775\pi$
$74$	49152.1	+	85133.9i	1.04343	+	1.80727i
$75$	−3411.71	+	5909.26i	−0.0700357	+	0.121305i
$76$	−190275.			−3.77875
$77$		0			0
$78$	−35065.6			−0.652597
$79$	−3806.63	+	6593.27i	−0.0686234	+	0.118859i	−0.898296	−	0.439392i	$-0.855194\pi$
$79$	−3806.63	+	6593.27i	−0.0686234	+	0.118859i	0.829672	+	0.558251i	$0.188527\pi$
$80$	145682.	+	252329.i	2.54496	+	4.40800i
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$	98552.2	−	170697.i	1.61857	−	2.80345i
$83$	63725.4			1.01535			0.507677	−	0.861548i	$-0.330504\pi$
$83$	63725.4			1.01535			0.507677	+	0.861548i	$0.330504\pi$
$84$		0			0
$85$	−62265.5			−0.934761
$86$	−57714.1	+	99963.8i	−0.841465	+	1.45746i
$87$	−3321.58	−	5753.15i	−0.0470486	−	0.0814906i
$88$	−59370.6	−	102833.i	−0.817268	−	1.41555i
$89$	−23195.7	+	40176.1i	−0.310407	+	0.537641i	−0.978451	−	0.206481i	$-0.933799\pi$
$89$	−23195.7	+	40176.1i	−0.310407	+	0.537641i	0.668043	+	0.744122i	$0.267132\pi$
$90$	56472.0			0.734897
$91$		0			0
$92$	−181657.			−2.23759
$93$	11070.0	−	19173.7i	0.132721	−	0.229879i
$94$	−419.878	−	727.251i	−0.00490122	−	0.00848916i
$95$	−63629.0	−	110209.i	−0.723345	−	1.25287i
$96$	136848.	−	237027.i	1.51551	−	2.62495i
$97$	21461.2			0.231592			0.115796	−	0.993273i	$-0.463058\pi$
$97$	21461.2			0.231592			0.115796	+	0.993273i	$0.463058\pi$
$98$		0			0
$99$	−14053.1			−0.144107
$100$	−35319.9	+	61175.9i	−0.353199	+	0.611759i
$101$	−72966.4	−	126382.i	−0.711737	−	1.23277i	−0.964205	−	0.265160i	$-0.914575\pi$
$101$	−72966.4	−	126382.i	−0.711737	−	1.23277i	0.252467	−	0.967605i	$-0.418758\pi$
$102$	50306.4	+	87133.2i	0.478765	+	0.829245i
$103$	−82814.3	+	143439.i	−0.769152	+	1.33221i	0.168871	+	0.985638i	$0.445988\pi$
$103$	−82814.3	+	143439.i	−0.769152	+	1.33221i	−0.938023	+	0.346572i	$0.887346\pi$
$104$	−238341.			−2.16080
$105$		0			0
$106$	−309972.			−2.67952
$107$	−107524.	+	186237.i	−0.907918	+	1.57256i	−0.0909669	+	0.995854i	$0.528996\pi$
$107$	−107524.	+	186237.i	−0.907918	+	1.57256i	−0.816951	+	0.576707i	$0.804338\pi$
$108$	−33961.5	−	58823.1i	−0.280174	−	0.485276i
$109$	20232.0	+	35042.8i	0.163107	+	0.282509i	0.935981	−	0.352050i	$-0.114515\pi$
$109$	20232.0	+	35042.8i	0.163107	+	0.282509i	−0.772875	+	0.634559i	$0.781182\pi$
$110$	60479.0	−	104753.i	0.476566	−	0.825436i
$111$	79078.7			0.609189
$112$		0			0
$113$	−15002.6			−0.110528			−0.0552638	−	0.998472i	$-0.517600\pi$
$113$	−15002.6			−0.110528			−0.0552638	+	0.998472i	$0.517600\pi$
$114$	−102816.	+	178082.i	−0.740965	+	1.28339i
$115$	−60746.9	−	105217.i	−0.428331	−	0.741890i
$116$	−34386.8	−	59559.7i	−0.237272	−	0.410968i
$117$	−14103.9	+	24428.7i	−0.0952521	+	0.164981i
$118$	38683.6			0.255753
$119$		0			0
$120$	383840.			2.43331
$121$	65475.3	−	113406.i	0.406550	−	0.704165i
$122$	89260.7	+	154604.i	0.542951	+	0.940419i
$123$	−79278.2	−	137314.i	−0.472488	−	0.818374i
$124$	114602.	−	198497.i	0.669328	−	1.15931i
$125$	147490.			0.844280
$126$		0			0
$127$	118326.			0.650986			0.325493	−	0.945544i	$-0.394470\pi$
$127$	118326.			0.650986			0.325493	+	0.945544i	$0.394470\pi$
$128$	579737.	−	1.00413e6i	3.12756	−	5.41710i
$129$	46426.9	+	80413.7i	0.245638	+	0.425457i
$130$	−121395.	−	210263.i	−0.630004	−	1.09120i
$131$	109733.	−	190063.i	0.558673	−	0.967650i	−0.438935	−	0.898519i	$-0.644644\pi$
$131$	109733.	−	190063.i	0.558673	−	0.967650i	0.997608	−	0.0691309i	$-0.0220226\pi$
$132$	−145485.			−0.726749
$133$		0			0
$134$	−161256.			−0.775805
$135$	22713.8	−	39341.5i	0.107264	−	0.185787i
$136$	341932.	+	592244.i	1.58523	+	2.74570i
$137$	71991.5	+	124693.i	0.327702	+	0.567597i	0.982056	−	0.188592i	$-0.0603923\pi$
$137$	71991.5	+	124693.i	0.327702	+	0.567597i	−0.654353	+	0.756189i	$0.727059\pi$
$138$	−98158.7	+	170016.i	−0.438764	+	0.759962i
$139$	244306.			1.07250			0.536249	−	0.844060i	$-0.319841\pi$
$139$	244306.			1.07250			0.536249	+	0.844060i	$0.319841\pi$
$140$		0			0
$141$	−675.524			−0.00286150
$142$	−169709.	+	293945.i	−0.706293	+	1.22334i
$143$	30209.3	+	52324.0i	0.123538	+	0.213974i
$144$	−189364.	−	327989.i	−0.761013	−	1.31811i
$145$	22998.3	−	39834.1i	0.0908395	−	0.157339i
$146$	−960842.			−3.73052
$147$		0			0
$148$	818666.			3.07222
$149$	139885.	−	242287.i	0.516184	−	0.894057i	−0.483639	−	0.875267i	$-0.660685\pi$
$149$	139885.	−	242287.i	0.516184	−	0.894057i	0.999823	−	0.0187896i	$-0.00598127\pi$
$150$	38170.5	+	66113.3i	0.138516	+	0.239917i
$151$	100209.	+	173566.i	0.357653	+	0.619474i	0.987568	−	0.157190i	$-0.0502436\pi$
$151$	100209.	+	173566.i	0.357653	+	0.619474i	−0.629915	+	0.776664i	$0.716910\pi$
$152$	−698838.	+	1.21042e6i	−2.45340	+	4.24941i
$153$	80935.7			0.279519
$154$		0			0
$155$	153294.			0.512503
$156$	−146011.	+	252899.i	−0.480369	+	0.832023i
$157$	−235001.	−	407034.i	−0.760888	−	1.31790i	−0.942393	−	0.334507i	$-0.891430\pi$
$157$	−235001.	−	407034.i	−0.760888	−	1.31790i	0.181505	−	0.983390i	$-0.441903\pi$
$158$	42588.8	+	73766.0i	0.135723	+	0.235079i
$159$	−124675.	+	215943.i	−0.391099	+	0.677403i
$160$	1.89504e6			5.85218
$161$		0			0
$162$	−73404.9			−0.219754
$163$	293503.	−	508362.i	0.865253	−	1.49866i	−0.00154277	−	0.999999i	$-0.500491\pi$
$163$	293503.	−	508362.i	0.865253	−	1.49866i	0.866796	−	0.498663i	$-0.166176\pi$
$164$	−820732.	−	1.42155e6i	−2.38282	−	4.12717i
$165$	−48651.0	−	84266.0i	−0.139118	−	0.240959i
$166$	356482.	−	617445.i	1.00408	−	1.73911i
$167$	172819.			0.479513			0.239757	−	0.970833i	$-0.422932\pi$
$167$	172819.			0.479513			0.239757	+	0.970833i	$0.422932\pi$
$168$		0			0
$169$	−250019.			−0.673374
$170$	−348316.	+	603300.i	−0.924380	+	1.60107i
$171$	82707.9	+	143254.i	0.216300	+	0.374643i
$172$	480636.	+	832486.i	1.23878	+	2.14564i
$173$	2545.03	−	4408.12i	0.00646514	−	0.0111979i	−0.862775	−	0.505589i	$-0.831275\pi$
$173$	2545.03	−	4408.12i	0.00646514	−	0.0111979i	0.869240	+	0.494391i	$0.164609\pi$
$174$	−74324.2			−0.186105
$175$		0			0
$176$	−811204.			−1.97400
$177$	15559.1	−	26949.1i	0.0373294	−	0.0646564i
$178$	259515.	+	449493.i	0.613920	+	1.06334i
$179$	−121139.	−	209819.i	−0.282587	−	0.489455i	0.689434	−	0.724348i	$-0.257859\pi$
$179$	−121139.	−	209819.i	−0.282587	−	0.489455i	−0.972021	+	0.234894i	$0.924526\pi$
$180$	235146.	−	407285.i	0.540949	−	0.936951i
$181$	−492254.			−1.11684			−0.558422	−	0.829557i	$-0.688593\pi$
$181$	−492254.			−1.11684			−0.558422	+	0.829557i	$0.688593\pi$
$182$		0			0
$183$	143608.			0.316993
$184$	−667184.	+	1.15560e6i	−1.45278	+	2.51630i
$185$	273766.	+	474177.i	0.588099	+	1.01862i
$186$	−123851.	−	214517.i	−0.262494	−	0.454652i
$187$	86678.6	−	150132.i	0.181262	−	0.313956i
$188$	−6993.40			−0.0144309
$189$		0			0
$190$	−1.42377e6			−2.86125
$191$	101865.	−	176435.i	0.202041	−	0.349946i	−0.747145	−	0.664661i	$-0.768576\pi$
$191$	101865.	−	176435.i	0.202041	−	0.349946i	0.949186	+	0.314716i	$0.101909\pi$
$192$	−857768.	−	1.48570e6i	−1.67925	−	2.90855i
$193$	30530.2	+	52879.8i	0.0589979	+	0.102187i	0.894016	−	0.448035i	$-0.147876\pi$
$193$	30530.2	+	52879.8i	0.0589979	+	0.102187i	−0.835018	+	0.550223i	$0.814543\pi$
$194$	120055.	−	207941.i	0.229021	−	0.396675i
$195$	−195308.			−0.367818
$196$		0			0
$197$	457733.			0.840325			0.420162	−	0.907449i	$-0.361973\pi$
$197$	457733.			0.840325			0.420162	+	0.907449i	$0.361973\pi$
$198$	−78613.5	+	136163.i	−0.142506	+	0.246828i
$199$	135274.	+	234301.i	0.242148	+	0.419412i	0.961326	−	0.275414i	$-0.0888148\pi$
$199$	135274.	+	234301.i	0.242148	+	0.419412i	−0.719178	+	0.694826i	$0.755481\pi$
$200$	259445.	+	449371.i	0.458638	+	0.794384i
$201$	−64859.3	+	112340.i	−0.113235	+	0.196129i
$202$	−1.63271e6			−2.81533
$203$		0			0
$204$	837891.			1.40965
$205$	548913.	−	950746.i	0.912261	−	1.58008i
$206$	926532.	+	1.60480e6i	1.52122	+	2.63483i
$207$	78961.7	+	136766.i	0.128083	+	0.221846i
$208$	−814137.	+	1.41013e6i	−1.30478	+	2.25995i
$209$	354306.			0.561065
$210$		0			0
$211$	933127.			1.44289			0.721447	−	0.692469i	$-0.243477\pi$
$211$	933127.			1.44289			0.721447	+	0.692469i	$0.243477\pi$
$212$	−1.29070e6	+	2.23556e6i	−1.97236	+	3.41623i
$213$	136519.	+	236458.i	0.206179	+	0.357112i
$214$	1.20299e6	+	2.08364e6i	1.79567	+	3.11019i
$215$	−321454.	+	556775.i	−0.474267	+	0.821455i
$216$	−498933.			−0.727625
$217$		0			0
$218$	452713.			0.645182
$219$	−386464.	+	669375.i	−0.544501	+	0.943104i
$220$	−503662.	−	872368.i	−0.701588	−	1.21519i
$221$	−173984.	−	301349.i	−0.239623	−	0.415039i
$222$	442369.	−	766205.i	0.602424	−	1.04343i
$223$	−197037.			−0.265329			−0.132664	−	0.991161i	$-0.542353\pi$
$223$	−197037.			−0.265329			−0.132664	+	0.991161i	$0.542353\pi$
$224$		0			0
$225$	61410.9			0.0808703
$226$	−83925.2	+	145363.i	−0.109300	+	0.189314i
$227$	599193.	+	1.03783e6i	0.771795	+	1.33679i	0.936578	+	0.350458i	$0.113974\pi$
$227$	599193.	+	1.03783e6i	0.771795	+	1.33679i	−0.164784	+	0.986330i	$0.552693\pi$
$228$	856238.	+	1.48305e6i	1.09083	+	1.88937i
$229$	122034.	−	211370.i	0.153778	−	0.266351i	−0.778836	−	0.627228i	$-0.784189\pi$
$229$	122034.	−	211370.i	0.153778	−	0.266351i	0.932613	+	0.360877i	$0.117523\pi$
$230$	−1.35928e6			−1.69430
$231$		0			0
$232$	−505181.			−0.616207
$233$	76130.2	−	131861.i	0.0918686	−	0.159121i	−0.816429	−	0.577446i	$-0.804049\pi$
$233$	76130.2	−	131861.i	0.0918686	−	0.159121i	0.908297	+	0.418325i	$0.137383\pi$
$234$	157795.	+	273310.i	0.188389	+	0.326299i
$235$	−2338.63	−	4050.62i	−0.00276243	−	0.00478467i
$236$	161076.	−	278992.i	0.188257	−	0.326071i
$237$	68519.3			0.0792395
$238$		0			0
$239$	1.51074e6			1.71078			0.855390	−	0.517984i	$-0.173317\pi$
$239$	1.51074e6			1.71078			0.855390	+	0.517984i	$0.173317\pi$
$240$	1.31114e6	−	2.27096e6i	1.46933	−	2.54496i
$241$	−116469.	−	201731.i	−0.129172	−	0.223733i	0.794184	−	0.607678i	$-0.207899\pi$
$241$	−116469.	−	201731.i	−0.129172	−	0.223733i	−0.923356	+	0.383945i	$0.874565\pi$
$242$	−732542.	−	1.26880e6i	−0.804070	−	1.39269i
$243$	−29524.5	+	51137.9i	−0.0320750	+	0.0555556i
$244$	1.48670e6			1.59864
$245$		0			0
$246$	−1.77394e6			−1.86897
$247$	355587.	−	615895.i	0.370855	−	0.642339i
$248$	−841817.	−	1.45807e6i	−0.869138	−	1.50539i
$249$	−286764.	−	496690.i	−0.293107	−	0.507677i
$250$	825063.	−	1.42905e6i	0.834905	−	1.44610i
$251$	762727.			0.764161			0.382081	−	0.924129i	$-0.375208\pi$
$251$	762727.			0.764161			0.382081	+	0.924129i	$0.375208\pi$
$252$		0			0
$253$	338258.			0.332236
$254$	661921.	−	1.14648e6i	0.643757	−	1.11502i
$255$	280195.	+	485312.i	0.269842	+	0.467380i
$256$	−3.43630e6	−	5.95185e6i	−3.27711	−	5.67612i
$257$	−690559.	+	1.19608e6i	−0.652181	+	1.12961i	0.330412	+	0.943837i	$0.392812\pi$
$257$	−690559.	+	1.19608e6i	−0.652181	+	1.12961i	−0.982593	+	0.185773i	$0.940521\pi$
$258$	1.03885e6			0.971640
$259$		0			0
$260$	−2.02193e6			−1.85495
$261$	−29894.2	+	51778.3i	−0.0271635	+	0.0470486i
$262$	−1.22770e6	−	2.12643e6i	−1.10494	−	1.91381i
$263$	316805.	+	548723.i	0.282425	+	0.489174i	0.971981	−	0.235058i	$-0.0755279\pi$
$263$	316805.	+	548723.i	0.282425	+	0.489174i	−0.689557	+	0.724232i	$0.742195\pi$
$264$	−534335.	+	925496.i	−0.471850	+	0.817268i
$265$	−1.72647e6			−1.51023
$266$		0			0
$267$	417522.			0.358427
$268$	−671459.	+	1.16300e6i	−0.571061	+	0.989106i
$269$	10266.9	+	17782.7i	0.00865081	+	0.0149836i	0.870318	−	0.492489i	$-0.163913\pi$
$269$	10266.9	+	17782.7i	0.00865081	+	0.0149836i	−0.861668	+	0.507473i	$0.830580\pi$
$270$	−254124.	−	440155.i	−0.212147	−	0.367449i
$271$	1.10469e6	−	1.91339e6i	0.913732	−	1.58263i	0.104984	−	0.994474i	$-0.466521\pi$
$271$	1.10469e6	−	1.91339e6i	0.913732	−	1.58263i	0.808747	−	0.588156i	$-0.200146\pi$
$272$	4.67195e6			3.82892
$273$		0			0
$274$	1.61089e6			1.29625
$275$	65768.3	−	113914.i	0.0524427	−	0.0908334i
$276$	817454.	+	1.41587e6i	0.645938	+	1.11880i
$277$	339920.	+	588759.i	0.266181	+	0.461039i	0.967872	−	0.251442i	$-0.0809047\pi$
$277$	339920.	+	588759.i	0.266181	+	0.461039i	−0.701691	+	0.712481i	$0.747571\pi$
$278$	1.36665e6	−	2.36711e6i	1.06059	−	1.83699i
$279$	−199259.			−0.153253
$280$		0			0
$281$	−831855.			−0.628466			−0.314233	−	0.949346i	$-0.601747\pi$
$281$	−831855.			−0.628466			−0.314233	+	0.949346i	$0.601747\pi$
$282$	−3778.91	+	6545.26i	−0.00282972	+	0.00490122i
$283$	−1.15536e6	−	2.00114e6i	−0.857531	−	1.48529i	−0.874277	−	0.485427i	$-0.838664\pi$
$283$	−1.15536e6	−	2.00114e6i	−0.857531	−	1.48529i	0.0167465	−	0.999860i	$-0.494669\pi$
$284$	1.41332e6	+	2.44794e6i	1.03979	+	1.80097i
$285$	−572661.	+	991877.i	−0.417624	+	0.723345i
$286$	675968.			0.488665
$287$		0			0
$288$	−2.46326e6			−1.74996
$289$	210722.	−	364981.i	0.148411	−	0.257055i
$290$	−257306.	−	445667.i	−0.179662	−	0.311183i
$291$	−96575.3	−	167273.i	−0.0668550	−	0.115796i
$292$	−4.00089e6	+	6.92974e6i	−2.74599	+	4.75620i
$293$	1.54768e6			1.05321			0.526603	−	0.850111i	$-0.323465\pi$
$293$	1.54768e6			1.05321			0.526603	+	0.850111i	$0.323465\pi$
$294$		0			0
$295$	215459.			0.144148
$296$	3.00678e6	−	5.20789e6i	1.99468	−	3.45488i
$297$	63238.9	+	109533.i	0.0416000	+	0.0720533i
$298$	−1.56504e6	−	2.71073e6i	−1.02090	−	1.76826i
$299$	339481.	−	587998.i	0.219602	−	0.380363i
$300$	635759.			0.407840
$301$		0			0
$302$	2.24228e6			1.41473
$303$	−656698.	+	1.13743e6i	−0.410922	+	0.711737i
$304$	4.77425e6	+	8.26925e6i	2.96293	+	5.13195i
$305$	497162.	+	861109.i	0.306019	+	0.530040i
$306$	452757.	−	784198.i	0.276415	−	0.478765i
$307$	149665.			0.0906303			0.0453151	−	0.998973i	$-0.485571\pi$
$307$	149665.			0.0906303			0.0453151	+	0.998973i	$0.485571\pi$
$308$		0			0
$309$	1.49066e6			0.888140
$310$	857534.	−	1.48529e6i	0.506812	−	0.877824i
$311$	73243.5	+	126862.i	0.0429406	+	0.0743753i	0.886697	−	0.462351i	$-0.152994\pi$
$311$	73243.5	+	126862.i	0.0429406	+	0.0743753i	−0.843756	+	0.536726i	$0.819661\pi$
$312$	1.07253e6	+	1.85768e6i	0.623770	+	1.08040i
$313$	−159167.	+	275686.i	−0.0918319	+	0.159057i	−0.908282	−	0.418359i	$-0.862606\pi$
$313$	−159167.	+	275686.i	−0.0918319	+	0.159057i	0.816450	+	0.577416i	$0.195939\pi$
$314$	−5.25842e6			−3.00975
$315$		0			0
$316$	709349.			0.399615
$317$	−1.08296e6	+	1.87574e6i	−0.605291	+	1.04840i	0.386714	+	0.922200i	$0.373610\pi$
$317$	−1.08296e6	+	1.87574e6i	−0.605291	+	1.04840i	−0.992005	+	0.126196i	$0.959723\pi$
$318$	1.39487e6	+	2.41599e6i	0.773511	+	1.33976i
$319$	64030.8	+	110905.i	0.0352300	+	0.0610201i
$320$	5.93909e6	−	1.02868e7i	3.24224	−	5.61572i
$321$	1.93544e6			1.04837
$322$		0			0
$323$	−2.04055e6			−1.08828
$324$	−305654.	+	529408.i	−0.161759	+	0.280174i
$325$	−132012.	−	228652.i	−0.0693275	−	0.120079i
$326$	−3.28373e6	−	5.68759e6i	−1.71129	−	2.96404i
$327$	182088.	−	315385.i	0.0941697	−	0.163107i
$328$	−1.20575e7			−6.18830
$329$		0			0
$330$	−1.08862e6			−0.550291
$331$	1.27173e6	−	2.20270e6i	0.638005	−	1.10506i	−0.347865	−	0.937544i	$-0.613093\pi$
$331$	1.27173e6	−	2.20270e6i	0.638005	−	1.10506i	0.985870	−	0.167512i	$-0.0535733\pi$
$332$	−2.96874e6	−	5.14201e6i	−1.47818	−	2.56028i
$333$	−355854.	−	616357.i	−0.175858	−	0.304594i
$334$	966757.	−	1.67447e6i	0.474188	−	0.821318i
$335$	−898156.			−0.437260
$336$		0			0
$337$	−2.57641e6			−1.23578			−0.617888	−	0.786266i	$-0.712012\pi$
$337$	−2.57641e6			−1.23578			−0.617888	+	0.786266i	$0.712012\pi$
$338$	−1.39861e6	+	2.42247e6i	−0.665896	+	1.15337i
$339$	67511.8	+	116934.i	0.0319066	+	0.0552638i
$340$	2.90073e6	+	5.02421e6i	1.36085	+	2.35706i
$341$	−213398.	+	369616.i	−0.0993811	+	0.172133i
$342$	1.85068e6			0.855593
$343$		0			0
$344$	7.06108e6			3.21718
$345$	−546722.	+	946950.i	−0.247297	+	0.428331i
$346$	−28474.0	−	49318.4i	−0.0127867	−	0.0221472i
$347$	995177.	+	1.72370e6i	0.443687	+	0.768488i	0.997960	−	0.0638470i	$-0.0203369\pi$
$347$	995177.	+	1.72370e6i	0.443687	+	0.768488i	−0.554273	+	0.832335i	$0.687004\pi$
$348$	−309481.	+	536038.i	−0.136989	+	0.237272i
$349$	1.37419e6			0.603926			0.301963	−	0.953320i	$-0.402358\pi$
$349$	1.37419e6			0.603926			0.301963	+	0.953320i	$0.402358\pi$
$350$		0			0
$351$	253870.			0.109988
$352$	−2.63804e6	+	4.56923e6i	−1.13482	+	1.96556i
$353$	1.46833e6	+	2.54323e6i	0.627174	+	1.08630i	0.988116	+	0.153710i	$0.0491220\pi$
$353$	1.46833e6	+	2.54323e6i	0.627174	+	1.08630i	−0.360942	+	0.932588i	$0.617545\pi$
$354$	−174076.	−	301509.i	−0.0738297	−	0.127877i
$355$	−945243.	+	1.63721e6i	−0.398082	+	0.689498i
$356$	4.32242e6			1.80760
$357$		0			0
$358$	−2.71063e6			−1.11779
$359$	−692873.	+	1.20009e6i	−0.283738	+	0.491449i	−0.972302	−	0.233727i	$-0.924908\pi$
$359$	−692873.	+	1.20009e6i	−0.283738	+	0.491449i	0.688564	+	0.725175i	$0.258241\pi$
$360$	−1.72728e6	−	2.99173e6i	−0.702435	−	1.21665i
$361$	−847182.	−	1.46736e6i	−0.342144	−	0.592611i
$362$	−2.75368e6	+	4.76952e6i	−1.10444	+	1.91295i
$363$	−1.17855e6			−0.469443
$364$		0			0
$365$	−5.35167e6			−2.10260
$366$	803346.	−	1.39144e6i	0.313473	−	0.542951i
$367$	−1.82044e6	−	3.15310e6i	−0.705523	−	1.22200i	−0.966502	−	0.256658i	$-0.917379\pi$
$367$	−1.82044e6	−	3.15310e6i	−0.705523	−	1.22200i	0.260979	−	0.965344i	$-0.415955\pi$
$368$	4.55800e6	+	7.89469e6i	1.75451	+	3.03889i
$369$	−713504.	+	1.23582e6i	−0.272791	+	0.472488i
$370$	6.12583e6			2.32627
$371$		0			0
$372$	−2.06284e6			−0.772873
$373$	−2.07469e6	+	3.59347e6i	−0.772114	+	1.33734i	0.164289	+	0.986412i	$0.447467\pi$
$373$	−2.07469e6	+	3.59347e6i	−0.772114	+	1.33734i	−0.936402	+	0.350928i	$0.885866\pi$
$374$	−969766.	−	1.67968e6i	−0.358499	−	0.620939i
$375$	−663704.	−	1.14957e6i	−0.243723	−	0.422140i
$376$	−25685.2	+	44488.1i	−0.00936944	+	0.0162283i
$377$	257049.			0.0931457
$378$		0			0
$379$	−1.26316e6			−0.451711			−0.225856	−	0.974161i	$-0.572518\pi$
$379$	−1.26316e6			−0.451711			−0.225856	+	0.974161i	$0.572518\pi$
$380$	−5.92850e6	+	1.02685e7i	−2.10613	+	3.64793i
$381$	−532468.	−	922262.i	−0.187924	−	0.325493i
$382$	−1.13967e6	−	1.97396e6i	−0.399595	−	0.692119i
$383$	1.14094e6	−	1.97617e6i	0.397435	−	0.688377i	−0.595974	−	0.803004i	$-0.703234\pi$
$383$	1.14094e6	−	1.97617e6i	0.397435	−	0.688377i	0.993409	+	0.114627i	$0.0365672\pi$
$384$	−1.04353e7			−3.61140
$385$		0			0
$386$	683148.			0.233371
$387$	417842.	−	723723.i	0.141819	−	0.245638i
$388$	−999801.	−	1.73171e6i	−0.337159	−	0.583976i
$389$	−1.62934e6	−	2.82211e6i	−0.545932	−	0.945582i	−0.998548	−	0.0538762i	$-0.982842\pi$
$389$	−1.62934e6	−	2.82211e6i	−0.545932	−	0.945582i	0.452616	−	0.891706i	$-0.350491\pi$
$390$	−1.09256e6	+	1.89237e6i	−0.363733	+	0.630004i
$391$	−1.94812e6			−0.644428
$392$		0			0
$393$	−1.97519e6			−0.645100
$394$	2.56058e6	−	4.43505e6i	0.830993	−	1.43932i
$395$	237210.	+	410860.i	0.0764962	+	0.132495i
$396$	654684.	+	1.13395e6i	0.209794	+	0.363374i
$397$	2.24742e6	−	3.89265e6i	0.715663	−	1.23957i	−0.247040	−	0.969005i	$-0.579458\pi$
$397$	2.24742e6	−	3.89265e6i	0.715663	−	1.23957i	0.962703	−	0.270560i	$-0.0872089\pi$
$398$	3.02690e6			0.957835
$399$		0			0
$400$	3.54490e6			1.10778
$401$	−276020.	+	478080.i	−0.0857194	+	0.148470i	−0.905698	−	0.423925i	$-0.860652\pi$
$401$	−276020.	+	478080.i	−0.0857194	+	0.148470i	0.819978	+	0.572395i	$0.193986\pi$
$402$	725650.	+	1.25686e6i	0.223956	+	0.387903i
$403$	428339.	+	741904.i	0.131379	+	0.227554i
$404$	−6.79850e6	+	1.17753e7i	−2.07233	+	3.58939i
$405$	−408849.			−0.123858
$406$		0			0
$407$	−1.52442e6			−0.456160
$408$	3.07739e6	−	5.33019e6i	0.915233	−	1.58523i
$409$	−3.02619e6	−	5.24152e6i	−0.894517	−	1.54935i	−0.834402	−	0.551157i	$-0.814187\pi$
$409$	−3.02619e6	−	5.24152e6i	−0.894517	−	1.54935i	−0.0601148	−	0.998191i	$-0.519147\pi$
$410$	−6.14128e6	−	1.06370e7i	−1.80426	−	3.12507i
$411$	647923.	−	1.12224e6i	0.189199	−	0.327702i
$412$	1.54321e7			4.47901
$413$		0			0
$414$	1.76686e6			0.506641
$415$	1.98552e6	−	3.43903e6i	0.565920	−	0.980202i
$416$	5.29516e6	+	9.17149e6i	1.50019	+	2.59840i
$417$	−1.09937e6	−	1.90417e6i	−0.309603	−	0.536249i
$418$	1.98200e6	−	3.43293e6i	0.554834	−	0.961001i
$419$	−1.48630e6			−0.413592			−0.206796	−	0.978384i	$-0.566304\pi$
$419$	−1.48630e6			−0.413592			−0.206796	+	0.978384i	$0.566304\pi$
$420$		0			0
$421$	−1.40434e6			−0.386159			−0.193079	−	0.981183i	$-0.561847\pi$
$421$	−1.40434e6			−0.386159			−0.193079	+	0.981183i	$0.561847\pi$
$422$	5.21995e6	−	9.04121e6i	1.42687	−	2.47141i
$423$	3039.86	+	5265.19i	0.000826043	+	0.00143075i
$424$	9.48094e6	+	1.64215e7i	2.56116	+	4.43606i
$425$	−378779.	+	656064.i	−0.101722	+	0.176187i
$426$	3.05477e6			0.815557
$427$		0			0
$428$	2.00367e7			5.28709
$429$	271884.	−	470916.i	0.0713247	−	0.123538i
$430$	3.59645e6	+	6.22924e6i	0.938001	+	1.62467i
$431$	1.35087e6	+	2.33977e6i	0.350283	+	0.606709i	0.986299	−	0.164968i	$-0.0527519\pi$
$431$	1.35087e6	+	2.33977e6i	0.350283	+	0.606709i	−0.636016	+	0.771676i	$0.719419\pi$
$432$	−1.70428e6	+	2.95190e6i	−0.439371	+	0.761013i
$433$	−4.76987e6			−1.22261			−0.611304	−	0.791396i	$-0.709355\pi$
$433$	−4.76987e6			−1.22261			−0.611304	+	0.791396i	$0.709355\pi$
$434$		0			0
$435$	−413969.			−0.104892
$436$	1.88507e6	−	3.26504e6i	0.474910	−	0.822569i
$437$	−1.99078e6	−	3.44813e6i	−0.498678	−	0.863735i
$438$	4.32379e6	+	7.48902e6i	1.07691	+	1.86526i
$439$	−3163.74	+	5479.77i	−0.000783502	+	0.00135707i	−0.866417	−	0.499321i	$-0.833583\pi$
$439$	−3163.74	+	5479.77i	−0.000783502	+	0.00135707i	0.865633	+	0.500678i	$0.166916\pi$
$440$	−7.39935e6			−1.82206
$441$		0			0
$442$	−3.89309e6			−0.947848
$443$	−707944.	+	1.22620e6i	−0.171392	+	0.296859i	−0.938907	−	0.344172i	$-0.888160\pi$
$443$	−707944.	+	1.22620e6i	−0.171392	+	0.296859i	0.767515	+	0.641031i	$0.221493\pi$
$444$	−3.68400e6	−	6.38087e6i	−0.886874	−	1.53611i
$445$	1.44544e6	+	2.50357e6i	0.346019	+	0.599322i
$446$	−1.10223e6	+	1.90912e6i	−0.262383	+	0.454460i
$447$	−2.51792e6			−0.596038
$448$		0			0
$449$	−1.88150e6			−0.440442			−0.220221	−	0.975450i	$-0.570678\pi$
$449$	−1.88150e6			−0.440442			−0.220221	+	0.975450i	$0.570678\pi$
$450$	343535.	−	595019.i	0.0799722	−	0.138516i
$451$	1.52826e6	+	2.64703e6i	0.353799	+	0.612798i
$452$	698919.	+	1.21056e6i	0.160909	+	0.278703i
$453$	901877.	−	1.56210e6i	0.206491	−	0.357653i
$454$	1.34076e7			3.05290
$455$		0			0
$456$	1.25791e7			2.83294
$457$	−3.72211e6	+	6.44688e6i	−0.833678	+	1.44397i	0.0614236	+	0.998112i	$0.480436\pi$
$457$	−3.72211e6	+	6.44688e6i	−0.833678	+	1.44397i	−0.895102	+	0.445861i	$0.852897\pi$
$458$	−1.36533e6	−	2.36482e6i	−0.304140	−	0.526786i
$459$	−364211.	−	630831.i	−0.0806902	−	0.139760i
$460$	−5.65996e6	+	9.80334e6i	−1.24715	+	2.16013i
$461$	7.95698e6			1.74380			0.871899	−	0.489686i	$-0.162888\pi$
$461$	7.95698e6			1.74380			0.871899	+	0.489686i	$0.162888\pi$
$462$		0			0
$463$	6.64462e6			1.44051			0.720257	−	0.693707i	$-0.244024\pi$
$463$	6.64462e6			1.44051			0.720257	+	0.693707i	$0.244024\pi$
$464$	−1.72562e6	+	2.98886e6i	−0.372092	+	0.644483i
$465$	−689824.	−	1.19481e6i	−0.147947	−	0.256252i
$466$	−851750.	−	1.47527e6i	−0.181697	−	0.314708i
$467$	1.48767e6	−	2.57671e6i	0.315655	−	0.546731i	−0.663921	−	0.747803i	$-0.731109\pi$
$467$	1.48767e6	−	2.57671e6i	0.315655	−	0.546731i	0.979577	+	0.201071i	$0.0644423\pi$
$468$	2.62820e6			0.554682
$469$		0			0
$470$	−52329.5			−0.0109270
$471$	−2.11501e6	+	3.66330e6i	−0.439299	+	0.760888i
$472$	−1.18319e6	−	2.04935e6i	−0.244456	−	0.423410i
$473$	−894980.	−	1.55015e6i	−0.183933	−	0.318582i
$474$	383299.	−	663894.i	0.0783596	−	0.135723i
$475$	−1.54829e6			−0.314861
$476$		0			0
$477$	2.24415e6			0.451602
$478$	8.45112e6	−	1.46378e7i	1.69178	−	2.93025i
$479$	1.70429e6	+	2.95192e6i	0.339395	+	0.587849i	0.984319	−	0.176398i	$-0.0564445\pi$
$479$	1.70429e6	+	2.95192e6i	0.339395	+	0.587849i	−0.644924	+	0.764246i	$0.723111\pi$
$480$	−8.52767e6	−	1.47704e7i	−1.68938	−	2.92609i
$481$	−1.52993e6	+	2.64991e6i	−0.301514	+	0.522238i
$482$	−2.60614e6			−0.510951
$483$		0			0
$484$	−1.22010e7			−2.36747
$485$	668677.	−	1.15818e6i	0.129081	−	0.223575i
$486$	330322.	+	572135.i	0.0634377	+	0.109877i
$487$	−2.95653e6	−	5.12087e6i	−0.564886	−	0.978410i	−0.997060	−	0.0766206i	$-0.975587\pi$
$487$	−2.95653e6	−	5.12087e6i	−0.564886	−	0.978410i	0.432175	−	0.901790i	$-0.357746\pi$
$488$	5.46034e6	−	9.45758e6i	1.03793	−	1.79776i
$489$	−5.28305e6			−0.999108
$490$		0			0
$491$	549890.			0.102937			0.0514686	−	0.998675i	$-0.483610\pi$
$491$	549890.			0.102937			0.0514686	+	0.998675i	$0.483610\pi$
$492$	−7.38658e6	+	1.27939e7i	−1.37572	+	2.38282i
$493$	−368772.	−	638731.i	−0.0683345	−	0.118359i
$494$	−3.97834e6	−	6.89068e6i	−0.733473	−	1.27041i
$495$	−437859.	+	758394.i	−0.0803195	+	0.139118i
$496$	−1.15021e7			−2.09929
$497$		0			0
$498$	−6.41668e6			−1.15941
$499$	−2.80472e6	+	4.85792e6i	−0.504241	+	0.873372i	0.495746	+	0.868467i	$0.334895\pi$
$499$	−2.80472e6	+	4.85792e6i	−0.504241	+	0.873372i	−0.999988	+	0.00490459i	$0.998439\pi$
$500$	−6.87102e6	−	1.19010e7i	−1.22913	−	2.12891i
$501$	−777686.	−	1.34699e6i	−0.138424	−	0.239757i
$502$	4.26672e6	−	7.39018e6i	0.755675	−	1.30887i
$503$	1.43167e6			0.252304			0.126152	−	0.992011i	$-0.459737\pi$
$503$	1.43167e6			0.252304			0.126152	+	0.992011i	$0.459737\pi$
$504$		0			0
$505$	−9.09381e6			−1.58678
$506$	1.89223e6	−	3.27743e6i	0.328546	−	0.569059i
$507$	1.12509e6	+	1.94870e6i	0.194386	+	0.336687i
$508$	−5.51240e6	−	9.54776e6i	−0.947724	−	1.64151i
$509$	2.69919e6	−	4.67513e6i	0.461784	−	0.799833i	−0.537266	−	0.843413i	$-0.680543\pi$
$509$	2.69919e6	−	4.67513e6i	0.461784	−	0.799833i	0.999050	+	0.0435796i	$0.0138762\pi$
$510$	6.26968e6			1.06738
$511$		0			0
$512$	−3.97880e7			−6.70775
$513$	744371.	−	1.28929e6i	0.124881	−	0.216300i
$514$	7.72602e6	+	1.33819e7i	1.28988	+	2.23413i
$515$	5.16057e6	+	8.93837e6i	0.857392	+	1.48505i
$516$	4.32573e6	−	7.49238e6i	0.715212	−	1.23878i
$517$	13022.2			0.00214269
$518$		0			0
$519$	−45810.6			−0.00746530
$520$	−7.42611e6	+	1.28624e7i	−1.20435	+	2.08600i
$521$	784443.	+	1.35870e6i	0.126610	+	0.219295i	0.922361	−	0.386329i	$-0.126257\pi$
$521$	784443.	+	1.35870e6i	0.126610	+	0.219295i	−0.795751	+	0.605624i	$0.792924\pi$
$522$	334459.	+	579300.i	0.0537237	+	0.0930523i
$523$	−2.31659e6	+	4.01246e6i	−0.370336	+	0.641440i	−0.989617	−	0.143729i	$-0.954091\pi$
$523$	−2.31659e6	+	4.01246e6i	−0.370336	+	0.641440i	0.619281	+	0.785169i	$0.287424\pi$
$524$	−2.04482e7			−3.25333
$525$		0			0
$526$	7.08888e6			1.11715
$527$	1.22902e6	−	2.12872e6i	0.192767	−	0.333882i
$528$	3.65042e6	+	6.32271e6i	0.569846	+	0.987002i
$529$	1.31756e6	+	2.28209e6i	0.204707	+	0.354563i
$530$	−9.65794e6	+	1.67280e7i	−1.49346	+	2.58676i
$531$	−280063.			−0.0431042
$532$		0			0
$533$	6.13515e6			0.935421
$534$	2.33563e6	−	4.04544e6i	0.354447	−	0.613920i
$535$	6.70037e6	+	1.16054e7i	1.01208	+	1.75297i
$536$	4.93224e6	+	8.54289e6i	0.741536	+	1.28438i
$537$	−1.09025e6	+	1.88837e6i	−0.163152	+	0.282587i
$538$	229733.			0.0342190
$539$		0			0
$540$	−4.23263e6			−0.624634
$541$	−5.18789e6	+	8.98568e6i	−0.762074	+	1.31995i	0.179705	+	0.983720i	$0.442486\pi$
$541$	−5.18789e6	+	8.98568e6i	−0.762074	+	1.31995i	−0.941780	+	0.336231i	$0.890848\pi$
$542$	−1.23594e7	−	2.14071e7i	−1.80717	−	3.13011i
$543$	2.21514e6	+	3.83674e6i	0.322405	+	0.558422i
$544$	1.51932e7	−	2.63155e7i	2.20117	−	3.81253i
$545$	2.52151e6			0.363638
$546$		0			0
$547$	1.07555e7			1.53695			0.768476	−	0.639879i	$-0.221015\pi$
$547$	1.07555e7			1.53695			0.768476	+	0.639879i	$0.221015\pi$
$548$	6.70766e6	−	1.16180e7i	0.954156	−	1.65265i
$549$	−646234.	−	1.11931e6i	−0.0915080	−	0.158497i
$550$	−735821.	−	1.27448e6i	−0.103721	−	0.179649i
$551$	753693.	−	1.30543e6i	0.105759	−	0.183179i
$552$	1.20093e7			1.67753
$553$		0			0
$554$	7.60610e6			1.05290
$555$	2.46389e6	−	4.26759e6i	0.339539	−	0.588099i
$556$	−1.13813e7	−	1.97130e7i	−1.56137	−	2.70437i
$557$	1.68656e6	+	2.92120e6i	0.230337	+	0.398955i	0.957907	−	0.287078i	$-0.0926839\pi$
$557$	1.68656e6	+	2.92120e6i	0.230337	+	0.398955i	−0.727570	+	0.686033i	$0.759351\pi$
$558$	−1.11466e6	+	1.93065e6i	−0.151551	+	0.262494i
$559$	−3.59286e6			−0.486308
$560$		0			0
$561$	−1.56021e6			−0.209304
$562$	−4.65342e6	+	8.05997e6i	−0.621487	+	1.07645i
$563$	4.88201e6	+	8.45589e6i	0.649124	+	1.12432i	0.983332	+	0.181817i	$0.0581977\pi$
$563$	4.88201e6	+	8.45589e6i	0.649124	+	1.12432i	−0.334209	+	0.942499i	$0.608469\pi$
$564$	31470.3	+	54508.1i	0.00416584	+	0.00721545i
$565$	−467444.	+	809637.i	−0.0616039	+	0.106701i
$566$	−2.58524e7			−3.39203
$567$		0			0
$568$	2.07633e7			2.70038
$569$	4.51973e6	−	7.82839e6i	0.585236	−	1.01366i	−0.409609	−	0.912261i	$-0.634335\pi$
$569$	4.51973e6	−	7.82839e6i	0.585236	−	1.01366i	0.994846	−	0.101398i	$-0.0323317\pi$
$570$	6.40697e6	+	1.10972e7i	0.825972	+	1.43063i
$571$	5.34963e6	+	9.26582e6i	0.686646	+	1.18931i	0.972916	+	0.231158i	$0.0742513\pi$
$571$	5.34963e6	+	9.26582e6i	0.686646	+	1.18931i	−0.286270	+	0.958149i	$0.592415\pi$
$572$	2.81469e6	−	4.87518e6i	0.359700	−	0.623019i
$573$	−1.83356e6			−0.233297
$574$		0			0
$575$	−1.47816e6			−0.186445
$576$	−7.71991e6	+	1.33713e7i	−0.969518	+	1.67925i
$577$	2.50031e6	+	4.33067e6i	0.312648	+	0.541521i	0.978935	−	0.204174i	$-0.0654508\pi$
$577$	2.50031e6	+	4.33067e6i	0.312648	+	0.541521i	−0.666287	+	0.745695i	$0.732117\pi$
$578$	−2.35757e6	−	4.08344e6i	−0.293525	−	0.508401i
$579$	274772.	−	475919.i	0.0340624	−	0.0589979i
$580$	−4.28563e6			−0.528987
$581$		0			0
$582$	−2.16098e6			−0.264450
$583$	2.40338e6	−	4.16278e6i	0.292854	−	0.507239i
$584$	2.93888e7	+	5.09028e7i	3.56574	+	6.17604i
$585$	878884.	+	1.52227e6i	0.106180	+	0.183909i
$586$	8.65780e6	−	1.49958e7i	1.04151	−	1.80395i
$587$	−7.54203e6			−0.903427			−0.451713	−	0.892163i	$-0.649187\pi$
$587$	−7.54203e6			−0.903427			−0.451713	+	0.892163i	$0.649187\pi$
$588$		0			0
$589$	5.02372e6			0.596674
$590$	1.20528e6	−	2.08761e6i	0.142547	−	0.246899i
$591$	−2.05980e6	−	3.56768e6i	−0.242581	−	0.420162i
$592$	−2.05414e7	−	3.55788e7i	−2.40894	−	4.17240i
$593$	2.99832e6	−	5.19324e6i	0.350139	−	0.606459i	−0.636134	−	0.771578i	$-0.719468\pi$
$593$	2.99832e6	−	5.19324e6i	0.350139	−	0.606459i	0.986274	+	0.165119i	$0.0528009\pi$
$594$	1.41504e6			0.164552
$595$		0			0
$596$	−2.60669e7			−3.00590
$597$	1.21746e6	−	2.10871e6i	0.139804	−	0.242148i
$598$	−3.79814e6	−	6.57856e6i	−0.434328	−	0.752278i
$599$	3.77075e6	+	6.53113e6i	0.429399	+	0.743740i	0.996820	−	0.0796875i	$-0.0253922\pi$
$599$	3.77075e6	+	6.53113e6i	0.429399	+	0.743740i	−0.567421	+	0.823428i	$0.692059\pi$
$600$	2.33500e6	−	4.04434e6i	0.264795	−	0.458638i
$601$	−2.34440e6			−0.264756			−0.132378	−	0.991199i	$-0.542261\pi$
$601$	−2.34440e6			−0.264756			−0.132378	+	0.991199i	$0.542261\pi$
$602$		0			0
$603$	1.16747e6			0.130753
$604$	9.33672e6	−	1.61717e7i	1.04136	−	1.80369i
$605$	−4.08009e6	−	7.06692e6i	−0.453191	−	0.784950i
$606$	7.34718e6	+	1.27257e7i	0.812717	+	1.40767i
$607$	−7.09702e6	+	1.22924e7i	−0.781816	+	1.35414i	0.149067	+	0.988827i	$0.452373\pi$
$607$	−7.09702e6	+	1.22924e7i	−0.781816	+	1.35414i	−0.930883	+	0.365318i	$0.880960\pi$
$608$	6.21037e7			6.81332
$609$		0			0
$610$	1.11246e7			1.21048
$611$	13069.3	−	22636.7i	0.00141628	−	0.00245307i
$612$	−3.77051e6	−	6.53071e6i	−0.406932	−	0.704826i
$613$	−7.68994e6	−	1.33194e7i	−0.826555	−	1.43164i	−0.900725	−	0.434390i	$-0.856964\pi$
$613$	−7.68994e6	−	1.33194e7i	−0.826555	−	1.43164i	0.0741701	−	0.997246i	$-0.476369\pi$
$614$	837229.	−	1.45012e6i	0.0896238	−	0.155233i
$615$	−9.88044e6			−1.05339
$616$		0			0
$617$	−3.26335e6			−0.345105			−0.172552	−	0.985000i	$-0.555201\pi$
$617$	−3.26335e6			−0.345105			−0.172552	+	0.985000i	$0.555201\pi$
$618$	8.33879e6	−	1.44432e7i	0.878277	−	1.52122i
$619$	5.73811e6	+	9.93869e6i	0.601924	+	1.04256i	0.992529	+	0.122005i	$0.0389325\pi$
$619$	5.73811e6	+	9.93869e6i	0.601924	+	1.04256i	−0.390605	+	0.920558i	$0.627734\pi$
$620$	−7.14144e6	−	1.23693e7i	−0.746116	−	1.29231i
$621$	710655.	−	1.23089e6i	0.0739486	−	0.128083i
$622$	1.63891e6			0.169855
$623$		0			0
$624$	1.46545e7			1.50664
$625$	5.78003e6	−	1.00113e7i	0.591875	−	1.02516i
$626$	1.78078e6	+	3.08440e6i	0.181624	+	0.314582i
$627$	−1.59438e6	−	2.76154e6i	−0.161965	−	0.280532i
$628$	−2.18957e7	+	3.79245e7i	−2.21544	+	3.83726i
$629$	8.77954e6			0.884800
$630$		0			0
$631$	9.11249e6			0.911095			0.455548	−	0.890211i	$-0.349444\pi$
$631$	9.11249e6			0.911095			0.455548	+	0.890211i	$0.349444\pi$
$632$	2.60528e6	−	4.51248e6i	0.259455	−	0.449389i
$633$	−4.19907e6	−	7.27300e6i	−0.416528	−	0.721447i
$634$	1.21162e7	+	2.09859e7i	1.19714	+	2.07351i
$635$	3.68675e6	−	6.38564e6i	0.362835	−	0.628449i
$636$	2.32327e7			2.27749
$637$		0			0
$638$	1.43276e6			0.139355
$639$	1.22867e6	−	2.12812e6i	0.119037	−	0.206179i
$640$	−3.61263e7	−	6.25726e7i	−3.48637	−	6.03857i
$641$	6.70607e6	+	1.16153e7i	0.644649	+	1.11656i	0.984383	+	0.176043i	$0.0563297\pi$
$641$	6.70607e6	+	1.16153e7i	0.644649	+	1.11656i	−0.339734	+	0.940522i	$0.610337\pi$
$642$	1.08269e7	−	1.87527e7i	1.03673	−	1.79567i
$643$	5.00517e6			0.477410			0.238705	−	0.971092i	$-0.423277\pi$
$643$	5.00517e6			0.477410			0.238705	+	0.971092i	$0.423277\pi$
$644$		0			0
$645$	5.78618e6			0.547637
$646$	−1.14149e7	+	1.97712e7i	−1.07620	+	1.86403i
$647$	2.91762e6	+	5.05346e6i	0.274011	+	0.474601i	0.969885	−	0.243563i	$-0.0783162\pi$
$647$	2.91762e6	+	5.05346e6i	0.274011	+	0.474601i	−0.695874	+	0.718164i	$0.744983\pi$
$648$	2.24520e6	+	3.88880e6i	0.210047	+	0.363813i
$649$	−299936.	+	519504.i	−0.0279522	+	0.0484147i
$650$	−2.95392e6			−0.274231
$651$		0			0
$652$	−5.46930e7			−5.03864
$653$	−7.56843e6	+	1.31089e7i	−0.694581	+	1.20305i	0.275741	+	0.961232i	$0.411077\pi$
$653$	−7.56843e6	+	1.31089e7i	−0.694581	+	1.20305i	−0.970322	+	0.241817i	$0.922257\pi$
$654$	−2.03721e6	−	3.52855e6i	−0.186248	−	0.322591i
$655$	−6.83799e6	−	1.18437e7i	−0.622766	−	1.07866i
$656$	−4.11865e7	+	7.13371e7i	−3.73676	+	6.47225i
$657$	6.95635e6			0.628736
$658$		0			0
$659$	1.26786e7			1.13725			0.568625	−	0.822597i	$-0.307475\pi$
$659$	1.26786e7			1.13725			0.568625	+	0.822597i	$0.307475\pi$
$660$	−4.53296e6	+	7.85131e6i	−0.405062	+	0.701588i
$661$	−700122.	−	1.21265e6i	−0.0623261	−	0.107952i	0.833179	−	0.553004i	$-0.186519\pi$
$661$	−700122.	−	1.21265e6i	−0.0623261	−	0.107952i	−0.895505	+	0.445052i	$0.853185\pi$
$662$	−1.42282e7	−	2.46439e7i	−1.26184	−	2.18557i
$663$	−1.56586e6	+	2.71214e6i	−0.138346	+	0.239623i
$664$	−4.36141e7			−3.83890
$665$		0			0
$666$	−7.96264e6			−0.695619
$667$	719554.	−	1.24630e6i	0.0626252	−	0.108470i
$668$	−8.05103e6	−	1.39448e7i	−0.698089	−	1.20912i
$669$	886664.	+	1.53575e6i	0.0765939	+	0.132664i
$670$	−5.02432e6	+	8.70238e6i	−0.432405	+	0.748947i
$671$	−2.76835e6			−0.237364
$672$		0			0
$673$	−6.01514e6			−0.511927			−0.255963	−	0.966686i	$-0.582393\pi$
$673$	−6.01514e6			−0.511927			−0.255963	+	0.966686i	$0.582393\pi$
$674$	−1.44125e7	+	2.49632e7i	−1.22205	+	2.11666i
$675$	−276349.	−	478650.i	−0.0233452	−	0.0404351i
$676$	1.16475e7	+	2.01741e7i	0.980316	+	1.69796i
$677$	3.30005e6	−	5.71585e6i	0.276725	−	0.479302i	−0.693844	−	0.720125i	$-0.744084\pi$
$677$	3.30005e6	−	5.71585e6i	0.276725	−	0.479302i	0.970569	+	0.240824i	$0.0774176\pi$
$678$	1.51065e6			0.126209
$679$		0			0
$680$	4.26150e7			3.53419
$681$	5.39273e6	−	9.34049e6i	0.445596	−	0.771795i
$682$	2.38751e6	+	4.13529e6i	0.196555	+	0.340443i
$683$	−106867.	−	185099.i	−0.00876581	−	0.0151828i	0.861609	−	0.507572i	$-0.169457\pi$
$683$	−106867.	−	185099.i	−0.00876581	−	0.0151828i	−0.870375	+	0.492389i	$0.836124\pi$
$684$	7.70614e6	−	1.33474e7i	0.629791	−	1.09083i
$685$	8.97230e6			0.730596
$686$		0			0
$687$	−2.19662e6			−0.177567
$688$	2.41196e7	−	4.17764e7i	1.94267	−	3.36480i
$689$	−4.82415e6	−	8.35567e6i	−0.387144	−	0.670553i
$690$	6.11676e6	+	1.05945e7i	0.489101	+	0.847148i
$691$	717549.	−	1.24283e6i	0.0571684	−	0.0990187i	−0.836025	−	0.548692i	$-0.815126\pi$
$691$	717549.	−	1.24283e6i	0.0571684	−	0.0990187i	0.893193	+	0.449673i	$0.148459\pi$
$692$	−474256.			−0.0376485
$693$		0			0
$694$	2.22682e7			1.75504
$695$	7.61195e6	−	1.31843e7i	0.597770	−	1.03537i
$696$	2.27331e6	+	3.93750e6i	0.177884	+	0.308104i
$697$	−8.80170e6	−	1.52450e7i	−0.686253	−	1.18863i
$698$	7.68727e6	−	1.33147e7i	0.597219	−	1.03441i
$699$	−1.37034e6			−0.106081
$700$		0			0
$701$	−1.27397e7			−0.979186			−0.489593	−	0.871951i	$-0.662855\pi$
$701$	−1.27397e7			−0.979186			−0.489593	+	0.871951i	$0.662855\pi$
$702$	1.42016e6	−	2.45979e6i	0.108766	−	0.188389i
$703$	8.97179e6	+	1.55396e7i	0.684685	+	1.18591i
$704$	1.65354e7	+	2.86401e7i	1.25743	+	2.17792i
$705$	−21047.6	+	36455.6i	−0.00159489	+	0.00276243i
$706$	3.28557e7			2.48084
$707$		0			0
$708$	−2.89937e6			−0.217380
$709$	−3.89752e6	+	6.75070e6i	−0.291187	+	0.504352i	−0.974091	−	0.226157i	$-0.927384\pi$
$709$	−3.89752e6	+	6.75070e6i	−0.291187	+	0.504352i	0.682903	+	0.730509i	$0.260717\pi$
$710$	1.05754e7	+	1.83172e7i	0.787323	+	1.36368i
$711$	−308337.	−	534055.i	−0.0228745	−	0.0396198i
$712$	1.58753e7	−	2.74968e7i	1.17360	−	2.03274i
$713$	4.79617e6			0.353322
$714$		0			0
$715$	3.76498e6			0.275422
$716$	−1.12869e7	+	1.95495e7i	−0.822795	+	1.42512i
$717$	−6.79832e6	−	1.17750e7i	−0.493860	−	0.855390i
$718$	7.75191e6	+	1.34267e7i	0.561174	+	0.971982i
$719$	−2.43480e6	+	4.21720e6i	−0.175647	+	0.304230i	−0.940385	−	0.340112i	$-0.889535\pi$
$719$	−2.43480e6	+	4.21720e6i	−0.175647	+	0.304230i	0.764738	+	0.644341i	$0.222868\pi$
$720$	−2.36005e7			−1.69664
$721$		0			0
$722$	−1.89567e7			−1.35338
$723$	−1.04823e6	+	1.81558e6i	−0.0745777	+	0.129172i
$724$	2.29324e7	+	3.97200e7i	1.62593	+	2.81620i
$725$	−279810.	−	484644.i	−0.0197705	−	0.0342435i
$726$	−6.59288e6	+	1.14192e7i	−0.464230	+	0.804070i
$727$	−1.29961e7			−0.911966			−0.455983	−	0.889989i	$-0.650712\pi$
$727$	−1.29961e7			−0.911966			−0.455983	+	0.889989i	$0.650712\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	−2.99374e7	+	5.18531e7i	−2.07925	+	3.60137i
$731$	5.15444e6	+	8.92776e6i	0.356770	+	0.617944i
$732$	−6.69017e6	−	1.15877e7i	−0.461487	−	0.799319i
$733$	2.40302e6	−	4.16215e6i	0.165195	−	0.286127i	−0.771529	−	0.636194i	$-0.780508\pi$
$733$	2.40302e6	−	4.16215e6i	0.165195	−	0.286127i	0.936725	+	0.350067i	$0.113841\pi$
$734$	−4.07344e7			−2.79075
$735$		0			0
$736$	5.92907e7			4.03452
$737$	1.25031e6	−	2.16559e6i	0.0847905	−	0.146862i
$738$	7.98273e6	+	1.38265e7i	0.539524	+	0.934483i
$739$	−9.28626e6	−	1.60843e7i	−0.625503	−	1.08340i	−0.988443	−	0.151591i	$-0.951560\pi$
$739$	−9.28626e6	−	1.60843e7i	−0.625503	−	1.08340i	0.362940	−	0.931813i	$-0.381773\pi$
$740$	2.55076e7	−	4.41804e7i	1.71234	−	2.96586i
$741$	−6.40057e6			−0.428226
$742$		0			0
$743$	1.17402e7			0.780192			0.390096	−	0.920774i	$-0.372442\pi$
$743$	1.17402e7			0.780192			0.390096	+	0.920774i	$0.372442\pi$
$744$	−7.57636e6	+	1.31226e7i	−0.501797	+	0.869138i
$745$	−8.71691e6	−	1.50981e7i	−0.575403	−	0.996627i
$746$	2.32118e7	+	4.02040e7i	1.52708	+	2.64498i
$747$	−2.58088e6	+	4.47021e6i	−0.169226	+	0.293107i
$748$	−1.61522e7			−1.05555
$749$		0			0
$750$	−1.48511e7			−0.964065
$751$	−7.52507e6	+	1.30338e7i	−0.486867	+	0.843279i	−0.999886	−	0.0150987i	$-0.995194\pi$
$751$	−7.52507e6	+	1.30338e7i	−0.486867	+	0.843279i	0.513019	+	0.858377i	$0.328527\pi$
$752$	175474.	+	303929.i	0.0113153	+	0.0195987i
$753$	−3.43227e6	−	5.94487e6i	−0.220594	−	0.382081i
$754$	1.43794e6	−	2.49059e6i	0.0921114	−	0.159542i
$755$	1.24890e7			0.797370
$756$		0			0
$757$	2.04785e6			0.129885			0.0649423	−	0.997889i	$-0.479314\pi$
$757$	2.04785e6			0.129885			0.0649423	+	0.997889i	$0.479314\pi$
$758$	−7.06617e6	+	1.22390e7i	−0.446695	+	0.773699i
$759$	−1.52216e6	−	2.63646e6i	−0.0959082	−	0.166118i
$760$	4.35481e7	+	7.54276e7i	2.73486	+	4.73692i
$761$	−8.25757e6	+	1.43025e7i	−0.516881	+	0.895264i	0.482927	+	0.875661i	$0.339574\pi$
$761$	−8.25757e6	+	1.43025e7i	−0.516881	+	0.895264i	−0.999808	+	0.0196033i	$0.993760\pi$
$762$	−1.19146e7			−0.743347
$763$		0			0
$764$	−1.89821e7			−1.17655
$765$	2.52175e6	−	4.36781e6i	0.155793	−	0.269842i
$766$	−1.27649e7	−	2.21095e7i	−0.786042	−	1.36147i
$767$	602040.	+	1.04276e6i	0.0369519	+	0.0640026i
$768$	−3.09267e7	+	5.35666e7i	−1.89204	+	3.27711i
$769$	2.10148e7			1.28147			0.640736	−	0.767761i	$-0.278629\pi$
$769$	2.10148e7			1.28147			0.640736	+	0.767761i	$0.278629\pi$
$770$		0			0
$771$	1.24301e7			0.753073
$772$	2.84459e6	−	4.92697e6i	0.171781	−	0.297534i
$773$	−1.39826e7	−	2.42186e7i	−0.841667	−	1.45781i	−0.888484	−	0.458907i	$-0.848241\pi$
$773$	−1.39826e7	−	2.42186e7i	−0.841667	−	1.45781i	0.0468169	−	0.998903i	$-0.485092\pi$
$774$	−4.67484e6	−	8.09706e6i	−0.280488	−	0.485820i
$775$	932532.	−	1.61519e6i	0.0557711	−	0.0965984i
$776$	−1.46882e7			−0.875616
$777$		0			0
$778$	−3.64584e7			−2.15948
$779$	1.79889e7	−	3.11576e7i	1.06209	−	1.83959i
$780$	9.09869e6	+	1.57594e7i	0.535479	+	0.927477i
$781$	−2.63171e6	−	4.55825e6i	−0.154387	−	0.267406i
$782$	−1.08979e7	+	1.88757e7i	−0.637272	+	1.10379i
$783$	538096.			0.0313657
$784$		0			0
$785$	−2.92882e7			−1.69636
$786$	−1.10493e7	+	1.91379e7i	−0.637936	+	1.10494i
$787$	1.33642e6	+	2.31475e6i	0.0769141	+	0.133219i	0.901917	−	0.431909i	$-0.142160\pi$
$787$	1.33642e6	+	2.31475e6i	0.0769141	+	0.133219i	−0.825003	+	0.565128i	$0.808827\pi$
$788$	−2.13242e7	−	3.69346e7i	−1.22337	−	2.11893i
$789$	2.85125e6	−	4.93850e6i	0.163058	−	0.282425i
$790$	5.30784e6			0.302587
$791$		0			0
$792$	9.61803e6			0.544845
$793$	−2.77836e6	+	4.81227e6i	−0.156894	+	0.271748i
$794$	−2.51443e7	−	4.35513e7i	−1.41543	−	2.45160i
$795$	7.76912e6	+	1.34565e7i	0.435967	+	0.755117i
$796$	1.26038e7	−	2.18305e7i	0.705051	−	1.22118i
$797$	8.17692e6			0.455978			0.227989	−	0.973664i	$-0.426785\pi$
$797$	8.17692e6			0.455978			0.227989	+	0.973664i	$0.426785\pi$
$798$		0			0
$799$	−74998.7			−0.00415611
$800$	1.15280e7	−	1.99672e7i	0.636840	−	1.10304i
$801$	−1.87885e6	−	3.25426e6i	−0.103469	−	0.179214i
$802$	3.08813e6	+	5.34879e6i	0.169535	+	0.293643i
$803$	7.44995e6	−	1.29037e7i	0.407722	−	0.706196i
$804$	1.20863e7			0.659404
$805$		0			0
$806$	9.58457e6			0.519679
$807$	92401.7	−	160045.i	0.00499455	−	0.00865081i
$808$	4.99388e7	+	8.64965e7i	2.69097	+	4.66090i
$809$	−1.18901e7	−	2.05942e7i	−0.638723	−	1.10630i	−0.985713	−	0.168432i	$-0.946130\pi$
$809$	−1.18901e7	−	2.05942e7i	−0.638723	−	1.10630i	0.346990	−	0.937869i	$-0.387204\pi$
$810$	−2.28711e6	+	3.96140e6i	−0.122483	+	0.212147i
$811$	2.42489e7			1.29461			0.647306	−	0.762231i	$-0.275896\pi$
$811$	2.42489e7			1.29461			0.647306	+	0.762231i	$0.275896\pi$
$812$		0			0
$813$	−1.98845e7			−1.05509
$814$	−8.52764e6	+	1.47703e7i	−0.451095	+	0.781319i
$815$	−1.82896e7	−	3.16786e7i	−0.964519	−	1.67060i
$816$	−2.10238e7	−	3.64143e7i	−1.10531	−	1.91446i
$817$	−1.05346e7	+	1.82465e7i	−0.552159	+	0.956367i
$818$	−6.77145e7			−3.53833
$819$		0			0
$820$	−1.02288e8			−5.31238
$821$	1.80055e6	−	3.11864e6i	0.0932280	−	0.161476i	−0.815640	−	0.578560i	$-0.803615\pi$
$821$	1.80055e6	−	3.11864e6i	0.0932280	−	0.161476i	0.908868	+	0.417085i	$0.136948\pi$
$822$	−7.24901e6	−	1.25557e7i	−0.374196	−	0.648127i
$823$	8.42191e6	+	1.45872e7i	0.433422	+	0.750709i	0.997165	−	0.0752410i	$-0.0239726\pi$
$823$	8.42191e6	+	1.45872e7i	0.433422	+	0.750709i	−0.563743	+	0.825950i	$0.690639\pi$
$824$	5.66787e7	−	9.81704e7i	2.90805	−	5.03689i
$825$	−1.18383e6			−0.0605556
$826$		0			0
$827$	−1.81504e7			−0.922829			−0.461415	−	0.887185i	$-0.652658\pi$
$827$	−1.81504e7			−0.922829			−0.461415	+	0.887185i	$0.652658\pi$
$828$	7.35709e6	−	1.27429e7i	0.372932	−	0.645938i
$829$	−5.36205e6	−	9.28735e6i	−0.270985	−	0.469359i	0.698130	−	0.715971i	$-0.254016\pi$
$829$	−5.36205e6	−	9.28735e6i	−0.270985	−	0.469359i	−0.969114	+	0.246612i	$0.920683\pi$
$830$	−2.22142e7	−	3.84761e7i	−1.11927	−	1.93863i
$831$	3.05928e6	−	5.29883e6i	0.153680	−	0.266181i
$832$	6.63806e7			3.32455
$833$		0			0
$834$	−2.45998e7			−1.22466
$835$	5.38461e6	−	9.32642e6i	0.267263	−	0.462912i
$836$	−1.65059e7	−	2.85890e7i	−0.816814	−	1.41476i
$837$	896666.	+	1.55307e6i	0.0442402	+	0.0766263i
$838$	−8.31442e6	+	1.44010e7i	−0.408999	+	0.708406i
$839$	1.18159e7			0.579510			0.289755	−	0.957101i	$-0.406426\pi$
$839$	1.18159e7			0.579510			0.289755	+	0.957101i	$0.406426\pi$
$840$		0			0
$841$	−1.99663e7			−0.973437
$842$	−7.85591e6	+	1.36068e7i	−0.381870	+	0.661419i
$843$	3.74335e6	+	6.48367e6i	0.181422	+	0.314233i
$844$	−4.34711e7	−	7.52941e7i	−2.10061	−	3.63836i
$845$	−7.78996e6	+	1.34926e7i	−0.375313	+	0.650061i
$846$	68020.3			0.00326748
$847$		0			0
$848$	1.29542e8			6.18615
$849$	−1.03982e7	+	1.80102e7i	−0.495096	+	0.857531i
$850$	4.23780e6	+	7.34009e6i	0.201184	+	0.348461i
$851$	8.56541e6	+	1.48357e7i	0.405438	+	0.702239i
$852$	1.27199e7	−	2.20315e7i	0.600322	−	1.03979i
$853$	6.26477e6			0.294803			0.147402	−	0.989077i	$-0.452909\pi$
$853$	6.26477e6			0.294803			0.147402	+	0.989077i	$0.452909\pi$
$854$		0			0
$855$	1.03079e7			0.482230
$856$	7.35903e7	−	1.27462e8i	3.43270	−	5.94562i
$857$	1.25568e7	+	2.17491e7i	0.584020	+	1.01155i	0.994997	+	0.0999068i	$0.0318545\pi$
$857$	1.25568e7	+	2.17491e7i	0.584020	+	1.01155i	−0.410977	+	0.911646i	$0.634812\pi$
$858$	−3.04185e6	−	5.26865e6i	−0.141065	−	0.244332i
$859$	−2.07327e6	+	3.59101e6i	−0.0958679	+	0.166048i	−0.909970	−	0.414673i	$-0.863896\pi$
$859$	−2.07327e6	+	3.59101e6i	−0.0958679	+	0.166048i	0.814103	+	0.580721i	$0.197229\pi$
$860$	5.99017e7			2.76180
$861$		0			0
$862$	3.02272e7			1.38557
$863$	6.90619e6	−	1.19619e7i	0.315654	−	0.546729i	−0.663922	−	0.747802i	$-0.731109\pi$
$863$	6.90619e6	−	1.19619e7i	0.315654	−	0.546729i	0.979576	+	0.201073i	$0.0644427\pi$
$864$	1.10847e7	+	1.91992e7i	0.505171	+	0.874982i
$865$	−158594.	−	274692.i	−0.00720685	−	0.0124826i
$866$	−2.66828e7	+	4.62160e7i	−1.20903	+	2.09410i
$867$	−3.79300e6			−0.171370
$868$		0			0
$869$	−1.32086e6			−0.0593345
$870$	−2.31576e6	+	4.01101e6i	−0.103728	+	0.179662i
$871$	−2.50965e6	−	4.34684e6i	−0.112090	−	0.194146i
$872$	−1.38469e7	−	2.39835e7i	−0.616682	−	1.06813i
$873$	−869178.	+	1.50546e6i	−0.0385987	+	0.0668550i
$874$	−4.45460e7			−1.97256
$875$		0			0
$876$	7.20160e7			3.17080
$877$	−4.57920e6	+	7.93141e6i	−0.201044	+	0.348218i	−0.948865	−	0.315682i	$-0.897767\pi$
$877$	−4.57920e6	+	7.93141e6i	−0.201044	+	0.348218i	0.747821	+	0.663900i	$0.231100\pi$
$878$	35396.2	+	61308.0i	0.00154960	+	0.00268399i
$879$	−6.96458e6	−	1.20630e7i	−0.304035	−	0.526603i
$880$	−2.52751e7	+	4.37777e7i	−1.10024	+	1.90566i
$881$	2.45789e7			1.06690			0.533449	−	0.845833i	$-0.320896\pi$
$881$	2.45789e7			1.06690			0.533449	+	0.845833i	$0.320896\pi$
$882$		0			0
$883$	−1.10185e7			−0.475575			−0.237787	−	0.971317i	$-0.576422\pi$
$883$	−1.10185e7			−0.475575			−0.237787	+	0.971317i	$0.576422\pi$
$884$	−1.62106e7	+	2.80776e7i	−0.697699	+	1.20845i
$885$	−969564.	−	1.67933e6i	−0.0416120	−	0.0720740i
$886$	7.92053e6	+	1.37188e7i	0.338977	+	0.587125i
$887$	−1.43491e7	+	2.48534e7i	−0.612374	+	1.06066i	0.378466	+	0.925615i	$0.376452\pi$
$887$	−1.43491e7	+	2.48534e7i	−0.612374	+	1.06066i	−0.990839	+	0.135047i	$0.956882\pi$
$888$	−5.41220e7			−2.30325
$889$		0			0
$890$	3.23433e7			1.36870
$891$	569150.	−	985797.i	0.0240178	−	0.0416000i
$892$	9.17924e6	+	1.58989e7i	0.386273	+	0.669045i
$893$	−76640.9	−	132746.i	−0.00321612	−	0.00557048i
$894$	−1.40854e7	+	2.43966e7i	−0.589419	+	1.02090i
$895$	−1.50976e7			−0.630013
$896$		0			0
$897$	−6.11065e6			−0.253575
$898$	−1.05252e7	+	1.82302e7i	−0.435551	+	0.754397i
$899$	907895.	+	1.57252e6i	0.0374659	+	0.0648929i
$900$	−2.86092e6	−	4.95525e6i	−0.117733	−	0.203920i
$901$	−1.38418e7	+	2.39747e7i	−0.568041	+	0.983876i
$902$	3.41966e7			1.39948
$903$		0			0
$904$	1.02679e7			0.417889
$905$	−1.53374e7	+	2.65651e7i	−0.622487	+	1.07818i
$906$	−1.00903e7	−	1.74768e7i	−0.408396	−	0.707363i
$907$	7.78185e6	+	1.34786e7i	0.314098	+	0.544033i	0.979245	−	0.202679i	$-0.0649647\pi$
$907$	7.78185e6	+	1.34786e7i	0.314098	+	0.544033i	−0.665148	+	0.746712i	$0.731631\pi$
$908$	5.58285e7	−	9.66979e7i	2.24720	−	3.89226i
$909$	1.18206e7			0.474491
$910$		0			0
$911$	2.36784e7			0.945273			0.472637	−	0.881257i	$-0.343302\pi$
$911$	2.36784e7			0.945273			0.472637	+	0.881257i	$0.343302\pi$
$912$	4.29683e7	−	7.44232e7i	1.71065	−	2.96293i
$913$	5.52801e6	+	9.57480e6i	0.219479	+	0.380148i
$914$	4.16432e7	+	7.21282e7i	1.64884	+	2.85588i
$915$	4.47445e6	−	7.74998e6i	0.176680	−	0.306019i
$916$	−2.27406e7			−0.895495
$917$		0			0
$918$	−8.14963e6			−0.319177
$919$	−6.59343e6	+	1.14202e7i	−0.257527	+	0.446050i	−0.965579	−	0.260111i	$-0.916241\pi$
$919$	−6.59343e6	+	1.14202e7i	−0.257527	+	0.446050i	0.708052	+	0.706160i	$0.249574\pi$
$920$	4.15756e7	+	7.20110e7i	1.61945	+	2.80498i
$921$	−673491.	−	1.16652e6i	−0.0261627	−	0.0453151i
$922$	4.45117e7	−	7.70964e7i	1.72443	−	2.98681i
$923$	−1.05649e7			−0.408188
$924$		0			0
$925$	6.66158e6			0.255990
$926$	3.71702e7	−	6.43807e7i	1.42452	−	2.46734i
$927$	−6.70796e6	−	1.16185e7i	−0.256384	−	0.444070i
$928$	1.12235e7	+	1.94396e7i	0.427817	+	0.741000i
$929$	−1.18400e7	+	2.05076e7i	−0.450105	+	0.779605i	−0.998392	−	0.0566850i	$-0.981947\pi$
$929$	−1.18400e7	+	2.05076e7i	−0.450105	+	0.779605i	0.548287	+	0.836290i	$0.315280\pi$
$930$	−1.54356e7			−0.585216
$931$		0			0
$932$	−1.41865e7			−0.534979
$933$	659192.	−	1.14175e6i	0.0247918	−	0.0429406i
$934$	−1.66441e7	−	2.88284e7i	−0.624300	−	1.08132i
$935$	−5.40138e6	−	9.35546e6i	−0.202058	−	0.349974i
$936$	9.65281e6	−	1.67192e7i	0.360134	−	0.623770i
$937$	9.81602e6			0.365247			0.182623	−	0.983183i	$-0.441541\pi$
$937$	9.81602e6			0.365247			0.182623	+	0.983183i	$0.441541\pi$
$938$		0			0
$939$	2.86501e6			0.106038
$940$	−217897.	+	377408.i	−0.00804324	+	0.0139313i
$941$	1.66086e7	+	2.87669e7i	0.611446	+	1.05906i	0.990997	+	0.133885i	$0.0427453\pi$
$941$	1.66086e7	+	2.87669e7i	0.611446	+	1.05906i	−0.379551	+	0.925171i	$0.623921\pi$
$942$	2.36629e7	+	4.09853e7i	0.868841	+	1.50488i
$943$	1.71740e7	−	2.97463e7i	0.628917	−	1.08932i
$944$	−1.61664e7			−0.590452
$945$		0			0
$946$	−2.00262e7			−0.727563
$947$	−3.69552e6	+	6.40082e6i	−0.133906	+	0.231932i	−0.925179	−	0.379531i	$-0.876085\pi$
$947$	−3.69552e6	+	6.40082e6i	−0.133906	+	0.231932i	0.791273	+	0.611463i	$0.209419\pi$
$948$	−3.19207e6	−	5.52883e6i	−0.115359	−	0.199808i
$949$	−1.49538e7	−	2.59007e7i	−0.538995	−	0.933568i
$950$	−8.66119e6	+	1.50016e7i	−0.311364	+	0.539299i
$951$	1.94933e7			0.698930
$952$		0			0
$953$	−1.81495e7			−0.647341			−0.323671	−	0.946170i	$-0.604917\pi$
$953$	−1.81495e7			−0.647341			−0.323671	+	0.946170i	$0.604917\pi$
$954$	1.25538e7	−	2.17439e7i	0.446587	−	0.773511i
$955$	−6.34770e6	−	1.09945e7i	−0.225220	−	0.390093i
$956$	−7.03799e7	−	1.21902e8i	−2.49060	−	4.31385i
$957$	576277.	−	998141.i	0.0203400	−	0.0352300i
$958$	3.81354e7			1.34250
$959$		0			0
$960$	−1.06904e8			−3.74381
$961$	1.12888e7	−	1.95528e7i	0.394311	−	0.682967i
$962$	1.71169e7	+	2.96474e7i	0.596332	+	1.03288i
$963$	−8.70946e6	−	1.50852e7i	−0.302639	−	0.524187i
$964$	−1.08518e7	+	1.87959e7i	−0.376105	+	0.651433i
$965$	3.80498e6			0.131533
$966$		0			0
$967$	3.12321e7			1.07408			0.537038	−	0.843558i	$-0.319543\pi$
$967$	3.12321e7			1.07408			0.537038	+	0.843558i	$0.319543\pi$
$968$	−4.48117e7	+	7.76162e7i	−1.53710	+	2.66234i
$969$	9.18248e6	+	1.59045e7i	0.314160	+	0.544140i
$970$	−7.48120e6	−	1.29578e7i	−0.255295	−	0.442184i
$971$	6.83554e6	−	1.18395e7i	0.232662	−	0.402982i	−0.725929	−	0.687770i	$-0.758590\pi$
$971$	6.83554e6	−	1.18395e7i	0.232662	−	0.402982i	0.958591	+	0.284788i	$0.0919232\pi$
$972$	5.50177e6			0.186783
$973$		0			0
$974$	−6.61558e7			−2.23445
$975$	−1.18811e6	+	2.05787e6i	−0.0400263	+	0.0693275i
$976$	−3.73034e7	−	6.46114e7i	−1.25350	−	2.17112i
$977$	−2.49513e7	−	4.32170e7i	−0.836291	−	1.44850i	−0.892975	−	0.450107i	$-0.851386\pi$
$977$	−2.49513e7	−	4.32170e7i	−0.836291	−	1.44850i	0.0566835	−	0.998392i	$-0.481947\pi$
$978$	−2.95536e7	+	5.11883e7i	−0.988013	+	1.71129i
$979$	−8.04866e6			−0.268390
$980$		0			0
$981$	−3.27758e6			−0.108738
$982$	3.07611e6	−	5.32797e6i	0.101794	−	0.176312i
$983$	1.10831e7	+	1.91965e7i	0.365828	+	0.633633i	0.988909	−	0.148525i	$-0.0474525\pi$
$983$	1.10831e7	+	1.91965e7i	0.365828	+	0.633633i	−0.623081	+	0.782158i	$0.714119\pi$
$984$	5.42586e7	+	9.39786e7i	1.78641	+	3.09415i
$985$	1.42618e7	−	2.47022e7i	0.468365	−	0.811232i
$986$	−8.25169e6			−0.270303
$987$		0			0
$988$	−6.62622e7			−2.15960
$989$	−1.00575e7	+	1.74200e7i	−0.326962	+	0.566315i
$990$	4.89880e6	+	8.48497e6i	0.158855	+	0.275145i
$991$	2.09458e7	+	3.62791e7i	0.677504	+	1.17347i	0.975730	+	0.218976i	$0.0702718\pi$
$991$	2.09458e7	+	3.62791e7i	0.677504	+	1.17347i	−0.298226	+	0.954495i	$0.596395\pi$
$992$	−3.74049e7	+	6.47872e7i	−1.20684	+	2.09031i
$993$	−2.28911e7			−0.736704
$994$		0			0
$995$	1.68592e7			0.539856
$996$	−2.67187e7	+	4.62781e7i	−0.853427	+	1.47818i
$997$	−2.11521e7	−	3.66364e7i	−0.673930	−	1.16728i	−0.976780	−	0.214243i	$-0.931272\pi$
$997$	−2.11521e7	−	3.66364e7i	−0.673930	−	1.16728i	0.302851	−	0.953038i	$-0.402062\pi$
$998$	3.13794e7	+	5.43508e7i	0.997284	+	1.72735i
$999$	−3.20269e6	+	5.54722e6i	−0.101531	+	0.175858i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.6.e.p.79.6		12
7.2	even	3		147.6.a.o.1.1	yes	6
7.3	odd	6		147.6.e.q.67.6		12
7.4	even	3	inner	147.6.e.p.67.6		12
7.5	odd	6		147.6.a.n.1.1	✓	6
7.6	odd	2		147.6.e.q.79.6		12
21.2	odd	6		441.6.a.ba.1.6		6
21.5	even	6		441.6.a.bb.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.6.a.n.1.1	✓	6	7.5	odd	6
147.6.a.o.1.1	yes	6	7.2	even	3
147.6.e.p.67.6		12	7.4	even	3	inner
147.6.e.p.79.6		12	1.1	even	1	trivial
147.6.e.q.67.6		12	7.3	odd	6
147.6.e.q.79.6		12	7.6	odd	2
441.6.a.ba.1.6		6	21.2	odd	6
441.6.a.bb.1.6		6	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	147.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(5.59404 - 9.68915i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-46.5865 - 80.6901i) q^{4} +(31.1575 - 53.9664i) q^{5} -100.693 q^{6} -684.407 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\)	\(q+(5.59404 - 9.68915i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-46.5865 - 80.6901i) q^{4} +(31.1575 - 53.9664i) q^{5} -100.693 q^{6} -684.407 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-348.592 - 603.780i) q^{10} +(86.7474 + 150.251i) q^{11} +(-419.278 + 726.211i) q^{12} +348.244 q^{13} -560.835 q^{15} +(-2337.83 + 4049.24i) q^{16} +(-499.603 - 865.338i) q^{17} +(453.117 + 784.821i) q^{18} +(1021.09 - 1768.57i) q^{19} -5806.07 q^{20} +1941.07 q^{22} +(974.835 - 1688.46i) q^{23} +(3079.83 + 5334.43i) q^{24} +(-379.079 - 656.585i) q^{25} +(1948.09 - 3374.19i) q^{26} +729.000 q^{27} +738.129 q^{29} +(-3137.33 + 5434.02i) q^{30} +(1229.99 + 2130.41i) q^{31} +(15205.3 + 26336.4i) q^{32} +(780.727 - 1352.26i) q^{33} -11179.2 q^{34} +7547.01 q^{36} +(-4393.26 + 7609.35i) q^{37} +(-11424.0 - 19786.9i) q^{38} +(-1567.10 - 2714.30i) q^{39} +(-21324.4 + 36935.0i) q^{40} +17617.4 q^{41} -10317.1 q^{43} +(8082.51 - 13999.3i) q^{44} +(2523.76 + 4371.28i) q^{45} +(-10906.5 - 18890.7i) q^{46} +(37.5291 - 65.0023i) q^{47} +42081.0 q^{48} -8482.34 q^{50} +(-4496.43 + 7788.04i) q^{51} +(-16223.5 - 28099.9i) q^{52} +(-13852.8 - 23993.7i) q^{53} +(4078.05 - 7063.39i) q^{54} +10811.3 q^{55} -18379.5 q^{57} +(4129.12 - 7151.85i) q^{58} +(1728.79 + 2994.35i) q^{59} +(26127.3 + 45253.9i) q^{60} +(-7978.20 + 13818.6i) q^{61} +27522.5 q^{62} +190615. q^{64} +(10850.4 - 18793.5i) q^{65} +(-8734.83 - 15129.2i) q^{66} +(-7206.58 - 12482.2i) q^{67} +(-46549.5 + 80626.1i) q^{68} -17547.0 q^{69} -30337.6 q^{71} +(27718.5 - 48009.8i) q^{72} +(-42940.5 - 74375.0i) q^{73} +(49152.1 + 85133.9i) q^{74} +(-3411.71 + 5909.26i) q^{75} -190275. q^{76} -35065.6 q^{78} +(-3806.63 + 6593.27i) q^{79} +(145682. + 252329. i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(98552.2 - 170697. i) q^{82} +63725.4 q^{83} -62265.5 q^{85} +(-57714.1 + 99963.8i) q^{86} +(-3321.58 - 5753.15i) q^{87} +(-59370.6 - 102833. i) q^{88} +(-23195.7 + 40176.1i) q^{89} +56472.0 q^{90} -181657. q^{92} +(11070.0 - 19173.7i) q^{93} +(-419.878 - 727.251i) q^{94} +(-63629.0 - 110209. i) q^{95} +(136848. - 237027. i) q^{96} +21461.2 q^{97} -14053.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 54 q^{3} - 150 q^{4} - 100 q^{5} + 36 q^{6} - 228 q^{8} - 486 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 - 54 * q^3 - 150 * q^4 - 100 * q^5 + 36 * q^6 - 228 * q^8 - 486 * q^9	\( 12 q - 2 q^{2} - 54 q^{3} - 150 q^{4} - 100 q^{5} + 36 q^{6} - 228 q^{8} - 486 q^{9} - 864 q^{10} - 604 q^{11} - 1350 q^{12} + 2704 q^{13} + 1800 q^{15} - 4578 q^{16} - 3028 q^{17} - 162 q^{18} - 1728 q^{19} + 904 q^{20} - 8232 q^{22} + 4484 q^{23} + 1026 q^{24} - 4806 q^{25} - 14172 q^{26} + 8748 q^{27} - 10640 q^{29} - 7776 q^{30} - 3976 q^{31} + 37326 q^{32} - 5436 q^{33} - 32672 q^{34} + 24300 q^{36} - 22680 q^{37} - 52744 q^{38} - 12168 q^{39} - 100600 q^{40} + 57512 q^{41} - 13536 q^{43} + 64940 q^{44} - 8100 q^{45} - 540 q^{46} - 51552 q^{47} + 82404 q^{48} - 81244 q^{50} - 27252 q^{51} - 119296 q^{52} - 80884 q^{53} - 1458 q^{54} + 23312 q^{55} + 31104 q^{57} + 70464 q^{58} - 8872 q^{59} - 4068 q^{60} - 50896 q^{61} + 23648 q^{62} + 399180 q^{64} - 3492 q^{65} + 37044 q^{66} - 6480 q^{67} - 37348 q^{68} - 80712 q^{69} - 221704 q^{71} + 9234 q^{72} - 64232 q^{73} + 27464 q^{74} - 43254 q^{75} - 389728 q^{76} + 255096 q^{78} - 111696 q^{79} + 308940 q^{80} - 39366 q^{81} + 189640 q^{82} + 202256 q^{83} - 46584 q^{85} - 3824 q^{86} + 47880 q^{87} + 97788 q^{88} + 35012 q^{89} + 139968 q^{90} - 898520 q^{92} - 35784 q^{93} + 121016 q^{94} + 119080 q^{95} + 335934 q^{96} + 141904 q^{97} + 97848 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 54 * q^3 - 150 * q^4 - 100 * q^5 + 36 * q^6 - 228 * q^8 - 486 * q^9 - 864 * q^10 - 604 * q^11 - 1350 * q^12 + 2704 * q^13 + 1800 * q^15 - 4578 * q^16 - 3028 * q^17 - 162 * q^18 - 1728 * q^19 + 904 * q^20 - 8232 * q^22 + 4484 * q^23 + 1026 * q^24 - 4806 * q^25 - 14172 * q^26 + 8748 * q^27 - 10640 * q^29 - 7776 * q^30 - 3976 * q^31 + 37326 * q^32 - 5436 * q^33 - 32672 * q^34 + 24300 * q^36 - 22680 * q^37 - 52744 * q^38 - 12168 * q^39 - 100600 * q^40 + 57512 * q^41 - 13536 * q^43 + 64940 * q^44 - 8100 * q^45 - 540 * q^46 - 51552 * q^47 + 82404 * q^48 - 81244 * q^50 - 27252 * q^51 - 119296 * q^52 - 80884 * q^53 - 1458 * q^54 + 23312 * q^55 + 31104 * q^57 + 70464 * q^58 - 8872 * q^59 - 4068 * q^60 - 50896 * q^61 + 23648 * q^62 + 399180 * q^64 - 3492 * q^65 + 37044 * q^66 - 6480 * q^67 - 37348 * q^68 - 80712 * q^69 - 221704 * q^71 + 9234 * q^72 - 64232 * q^73 + 27464 * q^74 - 43254 * q^75 - 389728 * q^76 + 255096 * q^78 - 111696 * q^79 + 308940 * q^80 - 39366 * q^81 + 189640 * q^82 + 202256 * q^83 - 46584 * q^85 - 3824 * q^86 + 47880 * q^87 + 97788 * q^88 + 35012 * q^89 + 139968 * q^90 - 898520 * q^92 - 35784 * q^93 + 121016 * q^94 + 119080 * q^95 + 335934 * q^96 + 141904 * q^97 + 97848 * q^99

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